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TEXT BOOK ON

MOTOR CAR ENGINEERING

I'EXT BOOK ON
MOTOR CAR ENGINEERING

TOLl'MK I.-a«STRUCTI()N
VOLUME II.-DESIGN

A. GEAHAM fiLAEK

VoLDME II.— DESIGN

NEW YORK

D. VAN NOSTRAND COMPANY

25 PARK PLACE

1917

BY THE SAME AUTHOR

TEXT-BOOK ON MOTOR CAR
ENGINEERING

Volume I.
CONSTRUCTION

Illustrated. Demy 8vo. 8*. Qd Net,

" The author has succeeded in produ3ing
a work which should prove of material
assistance to the student aod others
interested in motor-car construction." —
Engineering Review,

" The information cannot fail to be of
material benefit, as the whole of the
comprehensive subject has been well
covered." — The Engineer,

"We have pleasure in commending it
not only to the student who seeks
information on the thermodynamic and
constructional problems of this class of
internal - combustion engines and its
mountings, but also to the makers of
them. They will find much that will
interest and in many cases instruct
them." — Mechanical Engineer,

Printed in Great Britain.

PREFACE

This book is the second volume of a text book on Motor Gar
Engineering, and deals with the design of the petrol engine and
chassis. Yet, notwithstanding the fact' that the two volumes
must of necessity be complementary, an endeavour has been made
throughout the work to render it complete in itself, although
needless repetition has been avoided. It is anticipated, however,
that before students take up the study of design they will have
become well acquainted with the constructions commonly
employed. The Author has included a few of the illustrations
which appeared in the first volume. The subject-matter of this
volume has been written from the notes used by the Author in
his lecture to students on Motor Gar Design, and is intended for
the use of engineers, designers, draughtsmen, students and
others whose work entails a knowledge of design. The treat-
ment of the subject is from first principles, for two reasons:
firstly, because it enables a student to grasp the essentials and
the mode of application with less difficulty, and secondly, because
empirical formulsB, always dangerous, are especially so in
automobile design, where the conditions under which they are
used may vary so greatly from those under which they have
originated. Many worked examj)le8 have been given, which
should be read carefully by the reader.

The Author must again express his indebtedness to his friend
and colleague Mr. T. Wadhams, Wh. Ex., who has kindly checked
many of the calculations and read through the proofs, and to the
Institution of Givil Engineers, and the various firms who have
loaned him blocks for a number of the illustrations.

His best thanks are also due to the Gouncils of the Institution
of Givil Engineers and the American Society of Automobile
Engineers ; to the Engineering Standards Committee ; to the
Editor of the Practical Engineer's Pocket Book, and to Messrs.
Longmans, Green & Co. and Prof. A. Morley, B.Sc, for permission

')/**** r: i '^^

viii PEEFACE

to use matter from their publications and referred to in the text,
and to Mr. H. E. Wimperis, M.A., M.Inst.C.E., A.M.LE.E., for
information supplied.

It is hardly to be expected that the Author has been entirely
successful in avoiding mistakes in the calculations, and he would
therefore be glad to have any corrections brought to his notice.

PUBLISHERS' NOTE

Since this book was put in type the Author has joined the
army and his military duties have prevented his devoting time to
the correction of proofs for press.

This work has been undertaken by an eminent engineer who
is equally anxious with the publishers that, should any errors
have been inadvertently overlooked, the Author should not
receive the blame.

CONTENTS

PAGE

Pkefacb vii

List of Tables xiii

List op Illustrations xv

CHAPTER I

Introduction 1 — 10

General Bemarks on Design — ^Procedure in Design — Bases of
Design —Considerations in Design— Standardisation — Empirical
Formulee — Metric and English Units

CHAPTER II

Materials of Construction 11—54

Definitions — Resilience — Forms of Loading — Tension — Compres-
sion — Shear — Bending — Bending Moment — Shearing Force —
Torsion — Factors of Safety — Fluctuating and Alternating Stresses
— ^Impact Tests — Hardness Tests — ^Iron Ores — Cast Iron — Mal-
leable Cast Iron — ^Wrought Iron — Steel — Alloy Steels — Anneal-
ing — Case-hardening — Bronzes — Aluminium and its Alloys —
Bearing Metals.

CHAPTER III

General Considerations in Engine Design .... 65 — 76
Cooling — Lubrication — Number of Cylinders and Method of
Casting — Piston Speed — ^Revolutions and Stroke — Compression
Pressure — Type of Ignition — Tj'pe of Engine — Arrangement.

CHAPTER IV

Power Requirements 77— 9ft

Nature of the Resistances to be Overcome— Accelerometers —
Road Resistance — Gradient Resistance — Air Resistance — The
Efficiency of the Transmission — The Estimation of Power.

CHAPTER V

Determination of Engine Dimensions 100 — 112

Brake Horse-power in Terms of Engine Dimensions— Mechanical
Efficiency of the Engine — Mean Effective Pressure in the Cylinder
— Piston Speed— Compression Ratio — Cylinder Dimensions for a
stated Horse -power.

X CONTENTS

CHAPTER VI

PAGE

Oylinders and Valves 113—133

Material — Construction — Thicknesses of Cylinder Head, Walls,
etc. — "Water Jackets — Inlet and Exhaust Ports and Valves —
Cylinder Studs and Bolts.

CHAPTER VII

Valve Gears • . 134 — 158

Importance of, and desirable features in, a Good Valve Gear — i

Valve Timing — Valve Tappets— Cams — Design of Cam — Uniform
Acceleration — Simple Harmonia Motion — Valve Springs — Valve
Gear Arrangement — Camshaft — Sleeve, Piston and Rotary
Valves.

CHAPTER VIII

Pistons, Gudgeons and Connecting Rods .... 159 — 171

Mateiials for Piston — Piston Construction— Number and Dimen-
sions of Rings — Piston Thicknesses— Gudgeon Pin — Connecting
Rods — Loads on the Rod — The Design of the Rod.

CHAPTER IX

•Crankshafts and Fly-wheels 172—198

Material for Crankshaft —Arrangement — General Design of
Crankshaft — Formulae used for Shafts Subject to Combined Stress
— The Design of Crankshaft — Crankpin — Crankwebs — Crank-
journals — Couplings — Torsional Rigidity — Flywheels — Deter-
mination of Size of Flywheel.

CHAPTER X

The Balancing of Engines 199—220

Importance of a Good Balance — Balance of Single Rotating
Mass by a Single Mass — Balance of Two or more Co-planar
Rotating Classes — Refprence Plane— Balance of Single Mass by
two Separate Masses — Balance of a Number of Ro ating Masses
which are not Co-planar— Primarj- lialancing— Primary Balance
of Single Cylinder Engine — Primary Balance of an Engine with
more than One Cylinder — The Reciprocating and Rotating Parte
— Secondary Balancing — The Balance of a Six-Cylinder Engine.

CHAPTER XI

•Crankcases and Gearboxes 221 — 230

Materials— Crankcase Construction — Gearbox Construction —
General Note — Engine and Gearbox Suspensions.

CONTENTS xi

CHAPTEE xn

PAGE

ENGDfE Lubricating and Cooling Arrangements, Inlet, Exhaust

AND Fuel Piping, etc 231 — 247

Lubricating Arrangements — Details of Oil System — Oil Pumps
— General Bemarks — Engine Cooling — Air Cooling — Water
Cooling — ^Water Pumps — Radiators— Inlet and Exhaust Piping
— Fuel System.

CHAPTEE XIII

Clutches and Brakes 248 — 269

The Design of a Clutch — Cone Clutches— Multiple Disc Clutches
— Plate Clutches — Clutch Springs, Levers, etc. — Brakes — Opera-
ting (rear — Design of Brakes— Propeller Shaft Brakes— Boad
Wheel Brakes — Brake Cams— Springs, Levers, etc.

CHAPTER. XIV

Gearing 270—296

Types of Gears — Shapes of Teeth —Definitions — Cycloidal Teeth
— Involute Teeth — Methods of Measuring Pitch — Minimum
Number of Teeth — Proportions of Teeth — Design of Spur and
Bevel Gears — Helical Gearing — Worm Gearing- -Definitions —
Design of Worm Gear — Chain Drives — Points in Design of Chain
Drives.

CHAPTER XV

Transmission Gear 297—327

Load on Transmission Gear — Universal Joints — Design of
Universal Joints — Change Speed Gears — Arrangement and Details
of Gearbox — ^Number of Speeds and which Direct — Gear Ratios —
Oear Shafts — Propeller Shafts — Bevel and Worm Drives — Loads
on Bearings— Differential — Live Axle Shafts — Axle Casings —
Loads on Axle Casing — Cones, Keys and Feathers.

CHAPTER XVI

Frames, Axles and Springs— Torque and Radius Rods . 328 — 350

Frame Construction— Wheel Base and Track — Classification of

Load— Materials Employed — Frame Design — Helical Springs —

Plate Springs— Fixed Axles — Stub Axles — Torque Rods — Radius

Rods.

CHiVPTER XVII

Steering Gears 357 — 368

Geometrical Properties — Angles of Lock — Setting out Steering
Gear for Internal and External Systems— Steering Levers, Rods,
etc. — Steering Columns.

Appendix 1 — 18

Index 19—21

LIST OF TABLES

-NO.

II.

HI.

IV.

VI.

vn.

VIII.
IX.
IXa.
X.

XI-

XII.

XIII.
XIV.

XV.
XVI.

xvir.
xvin.

XIX.

XX.

XXI.

XXIL

XXIII.

XXIV.

XXV.

XXVI.

xxvn.
xxvra.

PAGE

Bending Moment and Deflection of Beams . . .19

Moments of Inertia, Moduli of Section and Radii of Gyration 20

Effect of Method of Loading upon Maximum Stress . . 27

Strengths of Materials, Elastic Limit, etc 29

Ultimate Tensile Strengths, etc., of Various Alloys . . 30
Iron and Steel Specifications of the A.S.A.E. . . .31
Tensile Strengths, etc., of Steels used in Motor Car

Construction 38

Tensile Strengths, etc., of Steels used in Motor Car

Construction 38

Tensile Strengths, etc., of Steels used in Motor Car

Construction 40

Tensile Strengths, etc., of Steels used in Motor Car

Construction 41

Air Pressure on the Front and Bear of Cars with Various

Profiles . . . • .86

Efficiencies of Transmission with Spur Wheel Gearbox 95

Valve Timing 137

Cylinder Operations for Given Crank Displacements . .180
Batio of Maximum to Mean Crank Effort and of Excess

Energy to Mean Energy 196

Cycloidal Cutters 274

Involute Cutters 276

Areas of Circles, advancing by Tenths . . Aj^pendix 1, 2

Circumferences of Circles, advancing by Tenths ,, 3, 4
Circumferences and Areas of Circles from ^ in.

to 5Jf in „ 6

Decimal Fractions of a Lineal Inch in Millimetres ,, 5

luchesandFractionswith Millimetre Equivalents ,, 6,7

Equivalent Values of Millimetres and Inches . „ 8

Pounds in Ejllogrammes ,, 9

Kilogrammes in Pounds ,, 9

Pounds per Square Inch in Kilogrammes per

Square Centimetre ,, 10

Imperial Standard Wire Gauge . ,, 10

Decimal Equivalents (Sixty-Fourths) . ,, H

Circular, Diametral and Metric Pitches . ,, H

XIV

LIST OF TABLES

NO.

XXIX.

XXX.

XXXI.

XXXIL

XXXIII.

XXXIV.

XXXV.

XXXVI.

XXXVII.

PAGE

Metric 60° Screw Threads Appendix 12

British Standard Castle Nuts . . - ,, 12

British Standard Automobile Threads . . ,, 13
British Standard Automobile Nuts and Bolt-

Heads ,, 13

British Standard Whitworth Thread . . ,.14

British Standard Pipe Threads . ... ,, 14

British Standard Fine Screw Threads . . ,, 15

Logaiithms „ 16, IT

Trigonometrical Hatios ,, 18

LIST OF ILLUSTRATIONS

FIG.

1. Sheffield Simplex Chassis

2. Bending Moments .

3. Shearing Moments

4. Longitudinal Section 30 h.-p. 1914 Sheffield Simpl

Self- starter

5. Cross-section 1913 Sheffield Simplex Engine

6. End View 1913 Sheffield Simplex Engine .

7. Cross-section 1914 Sheffield Simplex Engine

8- Profiles of Carriages

9. 12-16 Sunbeam Engine (1911)

10. 12-16 Sunbeam Cross-section (1911)

11. 25-30 Argyle Sleeve Valve ....

12. 12-16 Sunbeam Engine (1913) . . ' .

13. 12-16 Sunbeam Cross-section (1913)

14. Wolseley Valve and Tappet Gear '.

15. Cam Diagram ......

16. White and Poppe Camshaft Drive

17. Belsize and Crossley Camshaft Drives .

18. Eenold Camshaft Adjustment

19. Velocity and Acceleration Diagram for Valve Gear

20. Load Diagram for Valve Gear

21. Load on Connecting Bod ....

22. Stress Diagram for Shafts under Tortional Stress

23. Stress Diagram for Shafts under Combined Stress

24. Crankshafts .

25. Balancing Diagratn

26. Balancing Diagram

27. Balancing Diagram

28. Balancing Diagram

29. Balancing Diagram

30. Balancing Diagram

31. Balancing Diagram

32. Balancing Diagram

Frontispiece

ex Engine

with

PAGS

16
17

57
59
60
62
87
116
117
120
122
123
127
142
149
150
153
154
156
167
175
175
181
201
202
204
206
207
210
211
212

xvi LIST OF ILLUSTRATIONS

FIG. PAGE

•33. Balancing Diagram 217

54. Woleeley Combined Air and Oil Pump 235

35. Wolseley Centrifugal Pump 2-11

36. Wolseley Centrifugal Pump 242

37. 12-16 h.-p. Wolseley Clutch 250

38. 15-9 Armstrong- Whitworth Clutch 252

39. Argyle Plate Clutch 253

40. 12 h.-p. Eover Plate Qutch 254

41. Cone Clutch 256

42. Wolseley Propeller Shaft Brake 260

43. Armstrong- Whitworth Propeller Shaft Brake .... 261

44. Armstrong- Whitworth Eear Brakes 263

45. Wolseley Pedal Gear 268

46. Cycloidal Teeth 273

47. Involute Teeth 275

48. Worm Angle Diagrams . . . 287

49. Worm Angle Diagrams 288

50. Chain Driven Gearbox 294

51. 159 Armstrong-Whitworth Gearbox 301

52. 15-9 Armstrong-Whitworth Gearbox 303

53 20-28 Armstrong-Whitworth Gearbox 305

54. Sunbeam Gearbox 308

*55. Sunbeam Rear Axle 313

66. Armstrong- "^Tiitworth Rear Axle 317

67. Rover Rear Axle 320

68. Spring Shackle 332

59. Spring Shackle 336

60. Diagrams of B.M. and S.F. on Frame 339

61. Armstrong-Whitworth Front Axle and Steering Gear . , . 316

62. Sunbeam Front Axle and Steering Gear 347

63. Diagram of Steering Gear 360

64. Armstrong-Whitworth Steeling Gear 363

66. Armstrong-Whitworth Steering Column 364

66. Sunbeam Steering Column 366

MOTOE GAK ENGINEEEING

UME II)

<*t CHAPTER I

INTRODUCTION

1. Design is one of the most interesting branches of
engineering study, as while it presents the opportunity for
both ingenuity and originality, its application to practice is
immediately apparent. It must not be imagined, however, that
one can learn how to design a piece of machinery merely by
studying^ the theory of the subject, as facility in this branch of
work, as in others, can only be acquired by continual practice,
and theory has in some cases advanced insufficiently to render it
possible to rely upon it solely in practice. For this reason many
illustrations have been given in Volume I of this work ; these
/jjjf- should be thoroughly examined and the good features noted —
f^' * any improvements which may suggest themselves being carefully
and rigorously investigated, in order to ascertain whether they
are not accompanied by some disadvantages, having regard to
the fact that compromise plays no little part in many branches
of automobile design, and where the best arrangement has not
been selected it is often because the conditions are such as to
preclude the designer from making such a choice.

Frequent and critical reference to the technical press and to
actual examples must also be made, so that tried designs and
the trend of modern practice, may be gradually assimilated. The
practice of keeping notebooks in which any noteworthy feature
may be sketched and any data of interest to the designer entered
up is to be highly commended ; as although such books are easy
to compile, they will be found to be of great service in subsequent

H.G.B. B

2 .• • - : . MOTOR .GA^ ENGINEERING

work where the data available is scanty. It must be remembered,
however, that these sources of information cannot be made use
of to the fullest extent except by becoming thoroughly conversant
with the various entries therein through occasional perusal.

2. But such knowledge is not alone sufficient to ensure the
attainment of the highest degree of excellence, as the problems
met with in design call for many qualities that are not possessed .
by every engineer. Firstly, a designer should be endowed with
great powers of visualisation, so that he may have a clear con-
ception of the finished product before a pencil is put to paper.
In this the study of Descriptive Geometry is of inestimable service,
since it enables him to overcome the difficulties encountered in
picturing lines and surfaces in their relationship to one another,
and thus prepares him for the more practical work of mentally
depicting the various alternative arrangements, from which he
may choose that which is best for the particular conditions that
have to be satisfied.

Secondly, in no field of labour is it more essential that a
man should devote his whole time and energies to his work — he
should critically examine, not only the designs of others, but
those which he himself has produced, and devise means whereby
defects, if any, may be eliminated or improvements effected
when circumstances render it practicable to do so, as it is
impossible to reach the high standard of perfection which is now
demanded in first-class work without the exercise of considerable
thought and mental discussion. This work, it will be readily
seen, calls for far more than the ability to criticise — a fool can
destroy, but it requires a genius to create ; and if the design is
to represent an advance on an existing construction, not a slavish
copy of another model, it is essential that a designer should
originate. These remarks may be applied generally to the whole
chassis, but their particular application is to details, where
occasionally one sees contraptions on otherwise excellent designs,
which would never have been introduced had sufficient thought
been bestowed upon them in the initial stage.

Thirdly, since much of design is a compromise between that
which is eminently desirable and that which is practically
feasible, it is necessary that he should have had a sound practical
training supplemented by a varied experience, otherwise his
judgment may be defective, and he will be precluded from pro-

INTRODUCTION 8

dncing work that is cheap to manufacture, yet excellent in
construction and design — the cost of production being, generally,
of paramount importance, although luxury and finish or speed
may, under some circumstances, take priority. It should,
however, be clearly understood that cheapness is seldom, if ever,
synonymous with a low selling price ; because the cost of a car is
not determined by the latter alone, but in conjunction with
running expenses, repairs, and the rate at which depreciation
takes place, and these are not infrequently less with the more
expensive cars than with those sold at a lower figure. Hence,
a designer must always consider these other factors if his work
is intended to be of permanent value to a manufacturer. His
training and experience should have been such as to give him
an intimate knowledge of the capabilities and limitations of
machine tools, founding, smithing, die-forging and pressing, as
well as general workshop processes, but these will require
continual attention subsequently so that he may keep abreast with
modem improvements as they are introduced. This practical
experience is also .of service since it may enable him to detect an
error in his work that would pass unnoticed by a less qualified
man, and this is probably the reason why much of the rule-
of-thumb design prevalent at one time in other branches of
engineering work proved so satisfactory.

The need for thoroughness and for the exercise of care and
discrimination should also be emphasised, especially in regard
to details, as only by so doing can the perfection of the whole
be achieved. Not infrequently, a good general design suffers
through a lack of sufficient attention to the details of construc-
tion ; while attempts are sometimes made to introduce features
that, excellent in themselves, are quite out of place in the class
of engine or chassis under consideration.

The art of mental approximation is one that he should
continually practise, and it will be found to be of inestimable
service in design ; for although the use of the slide rule expedites
calculations, the actual paper work can be thereby materially
lessened, as it will then be unnecessary to wade through a large
number of figures, before a satisfactory result is obtained, when
adjusting the dimensions of the various parts. By continued
practice a high degree of accuracy can be attained even in more
or less complicated calculations.

4 MOTOE CAB ENGINEEEING

Lastly, the traditions of a firm must not be too lightly
esteemed. The reputation possessed by a car is built up after
long years of labour and depends for its continuance upon the
maintenance of the peculiar qualities upon which it has been
founded — namely, strong construction, reliability, silence, accessi-
bility, durability, efficiency, appearance, low running costs, etc.
All design is an evolution — a process in which defects are
eradicated and good features become established, and any
departure from past practice should be able to withstand the
severest scrutiny before introduction into any model. This con-
sideration is rendered all the more important from the fact that
any alterations are costly to initiate, in that fresh patterns, dies,
jigs, etc., are necessary ; and because those engaged in the shops
are not conversant with the new construction. Further, all
modifications must- be considered from the point of view of the
prospective purchaser, who is really the ultimate judge of the
wisdom of any change.

3. Having considered the qualities required for design,
reference may now be made to the drawing office. Without
depreciating in any way the care and thought bestowed by those
whose duty it is to superintend the construction of the chassis in
the shops, the drawing office is the brain of the works ; for there
the various processes to which the parts will be subjected during
manufacture should have been mentally performed during design,
in order that no drawing shall be sent out which will require
modification, owing to the resources of the workshops being
insufficient, or because of the impossibility of manufacturing such
a part except at great expense. It is, therefore, clear that it
is requisite for draughtsmen to have had a somewhat similar
training to that which has been already indicated. Attention
should be paid to the number and capacity of the machines in
the shops so that it will not be found that some machines are
glutted with work and others have little to do. It is not always
possible to do much in this direction, and it should not be allowed
to assume such an importance as to vitally affect the design,
but it is a point to bear in mind, as very little alteration is often
sufficient to render it easy to use another class of machine.

Attention must also be drawn to the importance of avoiding
the use of a large number of different sized nuts, which may or
may not require special spanners ; to the need for accuracy in

INTRODUCTION 6

dimensioning drawings and to the caution which should be exer-
cised in their final examination. Mistakes can be easily rectified
and modifications readily incorporated on paper, but they are apt
to prove expensive if delayed until after the work has been com-
menced in the shops. For this reason every endeavour should
be made to ensure that whatever leaves the drawing ofiSce is correct
in detail and represents the simplest, cheapest, and best con-
struction possible ; that sufficient views are given of every part
to clearly indicate the exact construction intended; that the
materials which are to be employed are specified ; that the pattern
or die number is quoted if the part is made from a pattern or a
die; that the series to which the drawing belongs and the number
of the particular part are given, and that all other information
required to enable the parts to be manufactured, without reference
to the drawing office, is given on the drawings. If these points
are attended to, the work is not only expedited, but the cost of
manufacture is also reduced.

In dimensioning drawings, care should be taken that the
figures are quite distinct and clear of any lines, especially where
the details are at all intricate or crowded, as may well happen if
the scale is rather small or if section lines are used. It is
preferable in such cases to re-draw the part to a larger scale on
the same drawing than that obscurity should exist. All measure-
ments should be inserted that are required to completely
dimension the drawing, and they should be such as will be
worked to in the shops; at the same time any unnecessary
duplication is to be avoided, as tending to cause complication
without serving any useful purpose. The distances should be
given from one flat machined surface or principal centre-line —
in many cases the former is to be preferred — but everything
depends upon the actual construction employed, us will not
involve the addition of or subtraction of dimensions, so as to
eliminate the possibility of error arising from mistakes made in
so doing.

4. Procedure in Design. — The procedure followed in originating
a design varies somewhat in practice; but generally, the conditions
to be fulfilled as to power, class and price as well as the principal
features to be embodied are formulated by the designer in
consultation with those with whom he is associated, and in
arriving at any decision the structural and manufacturing

6 MOTOR CAR ENGINEERING

advantages or disadvantages attaching to the varioas alternative
arrangements, methods of suspension, and construction of the
different members will have received consideration. Such a
survey is an important matter if the fullest advantage is to be
taken of modern developments in construction and design,
although it must be admitted that there will always be a natural
bias in favour of the retention of a construction which past
experience has proved to give highly satisfactory results.

These particulars are then expanded so as to more completely
specify the detail construction to be employed, and the kinds and
grades of materials which it is intended to use in the manufacture
of the various parts are selected, after which the full specifications
upon which the designs will be based may be drafted.

When the design of the constituent parts from strength or
other considerations has been completed, drawings should be
made to as large a scale as practicable from closely approximate,
if not the actual dimensions, and such modifications or special
features introduced as may be found to be either necessary or
desirable for the improvement or reducing the cost of the engine
or the chassis. These will practically determine the final con-
struction and the principal dimensions of at least the first car of
a type or series, but minor alterations may be subsequently
required if any imperfection that it is desirable to remove is
discovered.

In the design of details the greatest caution should be exer-
cised, as few parts can be regarded separately, but must be
considered in relation to contiguous portions of the engine or
chassis. For this reason it is desirable to make drawings show-
ing every part of importance in position, taking care that such
other parts as are essential to their efficient operation are also
included, the limits of action being indicated so as to ensure that
no moving member will foul another or have its motion limited
with the chassis loaded or unloaded, and that sufficient means
or opportunities for access and removal are provided, so that any
part that may require occasional attention can be readily dis-
mantled with the minimum of trouble. Especially is this so in
regard to the engine and the forward portion of the chassis, which,
from the multitude of parts there assembled that change their
relative position, require special attention in this respect. Care is
also necessary to ensure that there is sufficient clearance over the

INTRODUCTION 7

axles and propeller shaft when the springs are deflected to the
maximum extent. It will be obvious that much of this will be
unnecessary when the design is only a modification of a previous
model.

6. Consideratioiifl in Design. — It will be found that the con-
siderations which determine the dimensions given to the various
parts vary greatly in character, although strength is generally the
dominant factor. Thus, rigidity may have, and often has, as much
influence in the method of design, while occasionally appearance
or symmetry or practical considerations will necessitate an
increase in the size beyond that required for strength to resist
fracture alone. Mass may also, sometimes, be of greater
importance than any of these, as, for instance, in the flywheel.

That the general basis of design would be the resistance offered
to fracture is only to be expected, and in this connection it may
be noted that the desired strength may be obtained in two ways
— either by increasing the amount of metal in the part under
treatment or by choosing such a shape or section as will best
resist the straining action to which it is subjected. But as one
of the essential features of car construction is lightness, though
this must always remain subservient to strength and rigidity,
it is obvious that the latter method is much to be preferred.
With regard to the conditions under which rigidity is of greatest
consequence, it will be readily seen that undue flexure or distor-
tion should be avoided where bearings are to be supported or
where efficient working depends upon the correct alignment or
relative motion of two or more members, such as is found in
crankshafts, the transmission, the crank-case, the gear-box, and
the cam mechanism. The bearing areas and the thickness of the
water spaces round the cylinder afford two examples where
practical requirements limit the minimum dimensions — the
former, because practice shows that with any given system of
lubrication or kind of load, it is impossible to carry more than a
certain intensity of pressure for a given period of operation ; and
the latter, because the jacket core cannot be made less than a
certain thickness for any given size of cylinder without risk of
damage to it in the process of casting. The shape and extent
of a casting may also determine its general design, because of the
attention which must be given to the facility with which it may
be manufactured.

8 MOTOR CAR ENGINEERING

With many details, neither strength, rigidity nor practice can
determine the dimensions, as the load may be either so small as to
be quite negligible, or of such a character that its magnitude
cannot be determined or assumed. Under these circumstances,
an eye for symmetry is of great value and may be cultivated by a
studious examination of contemporaneous design. This may also
be applied to the complete chassis, as when well designed and pro-
portioned it should have a pleasing appearance, in which there
is an entire absence of any semblance of either cumbrousness or
weakness.

6. Standardisation. — With the object of reducing the cost of
manufacture, a system has been instituted in many works under
which certain component parts of a chassis are standardised. The
standardisation referred to is that which relates to a particular
works, not that which, is general in the industry, and it operates
in limiting the design, manufacture, and storage of a large number
of sizes of flanges, pipe connections, pins, studs, bolts, nuts, rods,
levers, etc. Such a system is to be highly commended, as it not
only benefits the manufacturer in the directions indicated but
also the owner and the repairer, since a large stock of these articles
and spanners is rendered unnecessary, and the cost of replace-
ment can be materially lessened. Great care is, however, required
in deciding the proportions and sizes of the parts in the first
instance, in order that a sufficient and suitable range may be
obtained ; otherwise some may be unduly cumbrous and others
too flimsy, having regard to the work they have to perform.
Recourse will, therefore, be made to tables giving the principal
dimensions of. these parts before insertion in the drawing, and
wherever possible the nearest size to that calculated will be
generally used, always having regard to the particular service to
which the part will be put. In some cases, cylinders, pistons,
valves, axles, etc., have been more or less standardised or rather
have been made suitable for several sizes of engine or chassis.
This is to some extent desirable from the point of view of first
cost, but it should not be allowed to restrict the design in any
way, although such is generally the tendency, because any
departure from the usual form necessarily involves an increased
cost of production.

Standardisation in regard to details has, however, made great
progress in the industry as a whole, as not only have threads of

INTRODUCTION 9

varioas sizes been standardised, but such parts as pipes, flanges,
wheels, ball and roller bearings, keyways and shafts, spanners,
lamp and step brackets, wheels and tyres, springs, etc., have also
received attention at the hands of both the S. M. M. T. and the
Engineering Standards Committee, the various bodies interested
having representatives on these Committees. These efforts can-
not fail to be of value to manufacturer and user alike, so long
as the standardisation is restricted to details of which a sufficient
range of sizes is provided, and a free hand is given to the designer
to develop his general design.

7. Empirical formulsB. — A word of warning may here be given
regarding the use of empirical formulae, as too often one finds
such a formula applied without discrimination to cases where
both the conditions of service and the materials employed vary
considerably and are entirely different from those under which
it was originated. Empirical formulae, as the adjective implies,
are based upon experience as distinct from theory, although
some may be shown to be rational and, therefore, are only of
service where the construction is similar, the loads are of a
like nature, and the materials used are of the same kind. To
illustrate this, a connecting rod designed for an engine having
a low speed of revolution is treated as a strut, and the inertia
loading entirely neglected. But in a fast-running engine, such
as is found in the modem car, the stress induced by the bending
moment on' the rod from its transverse acceleration may
amount to as much as, if not be more than that from the load
upon the piston ; consequently, any formula which ignores this
inertia force, though suitable for the first engine, would be
altogether valueless for the latter.

In some cases, however, on account of the extremely com-
plex nature of the conditions, the use of empirical formulae is
compulsory, but great care is necessary in their application, as
otherwise the result obtained will be quite valueless: for design
purposes.

8. Metric Units. — In the subsequent chapters of this book it will
be found that the ultimate tensile strengths and elastic limits of
materials as well as the permissible stresses, are quoted in English
units (pounds per square inch), but as the metric units are very
frequently employed in design, the metrical equivalents in kilo-
grammes per square centimetre have been added in brackets for

10 MOTOR CAR ENGINEERING

facility in working, while tables are given on pages 6, 7, 8, 9,
and 10 in the Appendix of metrical equivalents of English
measurements, etc. The procedure to be followed when using
these units in designing a part is exactly similar to that shown
in the text, provided that the loads and dimensions are in these
units. The metric system of measurement has much to re-
commend it for more extensive employment, as the troublesome
fractions of an inch which continually recur in design and call -
for the exercise of one's judgment are thereby almost entirely
obviated owing to their comparative unimportance, while many
of the specialities which are fitted are made to metric sizes.
Not only so, but the liability to mistakes occurring in the shops
is greatly reduced because of the elimination of the fractional
part, although much might be and is, sometimes, done by the
use of decimals in dimensioning drawings in English units. The
greatest objection to the system seems to be that some men are
not accustomed to working in these units, but this difficulty is
not insurmountable, and when once overcome the benefits
accruing therefrom more than compensate for any temporary
inconvenience occasioned by the change.

In obtaining the sizes of bolts or studs it is often found
that the use of the Whitworth thread reduces the sectional area
so much, that a larger diameter than is desirable becomes
necessary ; or that, owing to the excessive vibration to which it
is subjected, there is a possibility of the nut slacking back.
Under these circumstatices either a metric, a British Standard
Fine, or a special automobile thread is employed, and tables are
given on pages 14 and 15 in the Appendix which should facilitate
calculations. Metric threads for bolts and nuts are also often
employed because of their extensive use in Continental makes of
car, even where English units are employed elsewhere in the
design ; but this practice is not now so common as formerly.

CHAPTEE II

MATERIALS OF CONSTRUCTION

9. Among the many factors that have contributed to the
aucceas of the modern car is the excellence of the materials which
are available at the present day, and for this reason the science
of metallurgy is of the highest importance to the manufacturer
and designer. The choice of a material for any particular part
will be generally determined by the considerations referred to in
Art- 5 — strength, rigidity, lightness and good wearing qualities,
as well as reliability — but the facility with which it may be cast
or the ability to forge, weld, or press it into shape, are qualities
that require attention when deciding what material shall be used
in individual cases.

Before proceeding further it will be well to define some of the
terms used in the strength of materials.

10. DeflnitionB. — Stress is the mutual action and reaction
between the particles forming the material which enables them
to resist fracture. The intensity of stress is the load per unit of
area to which the material is subjected, and is usually expressed
in lbs. per square inch. It is commonly referred to as the
"stress." There are three forms of stress — compressive, tensile,
and shear. When the forces which produce the stress act
towards each other and along the axis of the member, they
induce a compressive stress in the material, but when they act
away from each other the stress is tensile. A shear stress is
produced when two equal and opposite tangential forces are
applied to two surfaces in the material indefinitely near to each
other ; a familiar example being that of a riveted lap-joint — the
part of the rivet between the plates is subjected to a shear stress.

Strain is the deformation produced by a stress. A bar of metal
under a compressive stress will decrease in length and increase in
diameter : while if the load is tensile, the bar will elongate and
decrease in diameter. The amount of shortening or lengthening
is termed the '* strain," and the alteration of length per unit length

12 MOTOR CAR ENGINEERING

is called the '* intensity of strain." The ratio between the intensity
of stress and the intensity of strain is known as the Direct
Modulus of Elasticity or Young^s Modulus,

Hookers Law — Within the elastic limit of a material, the strain
is proportional to the stress.

Hence, ^r-r rr^—r-c^ — — = E = Direct Modulus of Elasticity.

' Intensity of Strain "^

The angular movement in radians made by a line normal to the

two planes when the material is subjected to a shear stress is

called the shear strain, and the ratio between the shear stress and

shear strain is the Modulus of Rigidity or Shear Modulus, Thus,

Shear Stress ^t -^r j i ^ -n- -j-i
Shear Strain = ^ = ^°^"1°« ^* ^'^'^'^^-

The elastic limit of a material is the load per unit area which
can be applied to it without causing any permanent strain ; most
materials will, however, take a small amount of permanent
deformation when first subjected to a stress. The elastic limit is
generally from 40 to 50 per cent, of the ultimate tensile strength,
but in many of the higher grades of steel it reaches 80 or even
90 per cent. (See Tables VII. — IX. on p. 89, etc.) The elastic
limit has a great influence in determining the stress which is per-
missible in design, being as important as the ultimate tensile
strength, but because the commercial elastic limit may be arti-
ficially raised by straining beyond the yield point it is not always
relied upon as a proof of quality. A high elastic limit in conjunction
with a good elongation and reduction of area, however, generally
indicates a satisfactory material. In ascertaining the percentage
elongation, the observed length should be, preferably, from 8 to 10
times the diameter, as the local plastic flow from the larger mass
of metal near the grips prevents a true estimate of the ductility of
the metal from being obtained, when short specimens are tested.

It has been stated that when a bar is loaded, the elongation is
proportional to the stress up to the elastic limit ; but shortly after
this is passed there is usually an increment of strain without any
additional load — this is known as the yield point or commercial
elastic limit of the material.

If a cube of metal of 1 inch side is acted upon by a pressure on
each of its faces, as when placed within the cylinder of a hydraulic
press, it will diminish in volume. The volumetric change is called
the ** volumetric strain," and this has been found to be propor-

MATERIALS OP CONSTRUCTION

tional to the pressure on each face, which represents the stress.
The ratio between this stress and the rolametric strain is known as
the Bulk Modulibs or Modulus of Elasticity of Bulk or Cubic
Compressibility^ and therefore

1^ = K = Bulk Modulus.
Strain

A bar of metal under stress becomes longer or shorter accord-
ing as the stress is tensile or compressive, but this is accompanied
by a lateral contraction or a lateral dilation.

The relation between the lateral and the longitudinal strain is

called Poisson*s Ratio and is designated by — .

1= _2N__6Kjf2N
cr E - 2N 8K - 2N'

The following gives the values of — and o- for various materials : —

Steel .

Wrought iron .
Cast iron .
Copper and brass

0-308 — 0-27

0-278

0-81 - 0-28

0-25 — 0-45

8-30 — 8-72

8-6
8-28 - 4-85
40 — 2-22

The equations expressing the relations between E, N, and K

are: —

^ _ 2N (o- + 1) _ 9NK
o- 8K + N

o-E 8EK

N =

K =

2 (cr + 1)
crE

9K-E

8 ((T - 2) 9N - 8E
The ultimate strength of a material is the maximum load per
unit of area that it can support before fracture takes place. The
area of the section taken is the original sectional area of the bar.
Failing more definite data, it may be generally assumed, with steel
of ordinary composition, that the ultimate strength in compres-
sion is 0'9 and in shear 0*8 of the ultimate tensile strength.

14 MOTOE CAR ENGINEERING

11. Besilience. — The resilience of a body is the amount of
energy stored up in that body when loaded until the elastic limit
of the material is reached.

When a bar of metal is stretched, the magnitude of the work
done is one-half the product of the load and the elongation.
Thus, if W is the load, L the original length of the bar, I the
strain, A its sectional area and p the ultimate stress produced in
the material : —

,-W_-p, I
^- A-^L-

Work done = ^ WZ

_p^AL
■^ 2E

but since W = ^^A and Z = ^

Work done = ^ x volume of the bar,

and if / is the proof stress of the material, the proof resilience

is: —

^ X volume.

12. Forms of Loading.— In Art. 10 it has been explained that
when a material is subjected to a straining action, the stress
induced may be tensile, compressive or shear ; but it does not
follow from this that the force producing the stress is necessarily
pure tension, compression or shear. It is, therefore, requisite
that the various methods of loading should be considered, viz.,
tension, compression, shear, bending and torsion.

13. Tension. — ^When a bar of metal is subjected to a tensile
stress by a force P, the stress induced per unit area is found by
dividing P by the cross-sectional area of the bar, so that the

p
intensity of stress, /^ is equal to -r.

14. Compression. — In a similar manner the stress per unit area
may be found when the material of which the bar is composed
is in compression, provided that the ratio of this length to its
transverse dimensions is small. When, however, a long piece of
metal is under load, unless the distribution of stress is uniform,

MATERIALS OP CONSTRUCTION 16

tbafc is, anless the load is axially applied, the column will bend,
as one side of the section being more highly stressed will yield
more, and this bending will still further augment the eccentricity
of the loading by bringing the resultant thrust nearer to the side
having the greater stress, until at length the column fails
through bending or buckling. In practice loads are seldom
exactly central or symmetrical, neither are the end fixings
exactly true, nor the material of a homogeneous quality through-
out, BO that practically all columns fail under a lower stress than
when subjected to pure compression.

Several formula have been devised to represent the load at
which such a column will fail ; but that which is most generally'
adopted is due to Gordon and modified by Rankine. This formula
is of an empirical nature, being based upon experimental work, but
has a rational basis, and is applicable to many cases met with in
automobile design. It is as follows : —

P — ft

where F is the critical load in lb. or kilos.

A the cross-sectional area of the column (in in.^ or cm.^)
I the length of the column in ins. or cms.
a is a constant depending upon the material and the

method of fixing
h is the least radius of gyration, to be found from the
equation I = Afc*
The value of a for a steel column when hinged at both ends is

1 . i_

Q-^7^ ; when hinged at one end and fixed at the other 9 ^ q ^^^

1 1

jjg^^and when fixed at both ends = ^ , /, is determmed by

the material of which the column is made and may be taken to
be about two-thirds of its compressive strength.

15. Shear. — In the majority of cases the part under considera-
tion will be in double shear, that is, there will be two sections
subject to a shear stress. For single shear the intensity of stress
produced is found by dividing the load to which the pin or rivet
is subjected by its cross-sectional area. In the case of double

MOTOR CAR ENGINEERING

shear, the total area over which the load is distributed is twice
the cross-sectional area of the part, and therefore the stress will
apparently be one-half of that produced by single shear, but
owing to the bending which takes place along the pin, it is usual
to consider it as being only If times as strong as a pin in single
shear. The intensity of stress is therefore found as follows : —

•^ If A

16. Bending. — ^When a horizontal beam supported at the ends
is loaded by a weight or force P at some point in its length it
will bend, the upper fibres of the beam being in compression and
the lower fibres in tension, and
resulting in the shortening or
lengthening of the layers com-
posing the beam. It will be clear
that at some layer there will be
no alteration in length, and since,
within the elastic limit of the
material, the stress varies as the
strain, the distribution of stress
will not be uniform over the whole
sectional area, but decrease from
a maximum value at the upper
surface to zero at this layer (which is known as the neutral sur-
face), and then increase to a maximum again at the lower surface.
The line of intersection of the neutral surface with any transverse
section of the beam is called the neutral axis of the section.

17. Bending Moment. — The straining action at any particular
section of a beam will depend upon the magnitude and point of
application of the force or forces, the method of support and
the distances between the section considered and the points of
application of the forces. The tendency of these external forces
to bend the beam at any section is termed the " Bending Moment "
(M) ; and is the algebraic sum of the moments of the forces acting
on the beam on either side of the section considered.

For example, take the case of a beam freely supported at the ends — a
very usual condition — and carrying a single load W, as shown in Fig. 2,
where the weight of the beam is small compared with W. We may proceed
by finding the reactions at the points of support in the following manner —

FiQ. 2.

MATERIALS OF CONSTRUCTION

Taking moments about the right hand end of the beam —

W X /, = RiL and Ri = ^
also, taking moments about the left hand end of beam —

W X ^ = R^L and R, = ^

Then the bending moment at any point P —

= Ri X / - W(Z - /,)
or = Ra(L - /).

The maximum bending moment is at the point of application of the
load and its magnitude is Rj x ^ = R, x ^.

The curve ABC represents graphically the bending moment along

the beam and may be
obtained by finding
the bending moment
at the point of appli-
cation of the load,
setting up the ordinate
DB from AC, so that
DB represents the
bending moment at D
.to some suitable scale
and joining AB, BC.
The bending moment
curve will be formed
by the two straight
lines AB, BC, because
the bending moment
at any point is directly
proportional to . the distance between the point and the end of the beam
on the same side of the load as the point is situated.

If two or more concentrated loads W|, W,, W„ .... are applied, as
seen in Fig. 3, the curve of bending moment may be obtained as
follows : —

The reaction at the points of support may be determined in a
similar manner to that already described, namely, by taking moments
about one end of the beam.
Then Ri X L = (Wi X Z,) + (W, x h) + (W^ X h)

and Rj = Wi + W, + Ws - Ri.
The bendmg moment at B = W,(/i — l^ + Wb(/i - h) —B^X h

or = Ri(L - l^).

M.C.E. G

PlO. 3.

18 MOTOR CAB ENGINEERING

The bonding moment at C = Wj(/j — h) — B^ X h

or = R,(L - ;,) - W,(;, - h).

The bending moment atD = Rj x ^s

or = R,(L - h) - W,(^, - h) ^ W,{U - «.

At B, C and D draw BJ, CK and DL respectively perpendicular to
AE to represent to scale the calculated bending moments at these
points. Then the bending moment at any section will be given by the
length of the ordinate between AE and the lines joining AJKLE. The
curve of bending moment along the beam will be formed by straight
lines between successive points of loading because the curve of bending
moment for each separate concentrated load is formed by straight lines.

The bending moment at any point P

= (R, X AP) - (W, X BP)
or = (Rj X EP) ~ (W, X CP) - (W, X DP)

In some cases there are distributed loads as, for example, where tbe
^freight of the beam is considered. These may be dealt with after
replacing them by their resultant, thus : Let it be assumed in Fig. 2
that the weight of the beam is to per inch run so that the total weight
is wL, This is distributed equally between the supports and the

reactions due thereto are therefore -« • Hence Ri now becomes equal

WL , wL , ^ . , WL , wh _, ,, , ,.

to -y— -h -s- and R, is equal to -y- + -o-- Then the bendmg

moment at any point P will be : —

= R,; - W (/ - I,) - It'/ X I

= R,(L -I) - w{h - I) (^-^) .

It will be observed that the weight of the beam is replaced by two
equivalent concentrated loads acting at the centre of gravity of the
portions of the distributed load to the right and left of the section
considered.

The curve of bending moment for any number of loads may also be
obtained by considering each load separately and adding the bending
moment curves together, but it will, generally, be preferable to
proceed as previously indicated or to make use of the funicular polygon,
which will now be described in reference to the loading shown in Fig. 3.

Draw a vertical line MR to the right of the diagram of loads and
mark off MN to represent to scale Wj, NQ to represent Wj and QR to

MATERIALS OF CONSTRUCTION

represent W^ ; select any point such that its horizontal diBtance from
MN, the polar distance, represents, to some scale, the length of the
beam. Join M, N, Q and R to 0. Take any point A on a vertical line
drawn through the left hand point of support and draw AJ, JK, KL
and LE parallel to MO, NO, QO and RO respectively intersecting the
vertical lines drawn through the points of loading at J, K, L. Join AE
and draw XO parallel to AE. Then the bending moment at any section
along the beam is proportional to the length of the ordinate between
AE and AJKLE. It* magnitude may be obtained by multiplying the
length of the ordinate by the scale to which MR represents the scale of
loads and then by the length represented by the horizontal distance of
O from MR. The reactions, Rj, R^ at the points of support are given
to scale by the distances MX, XR respectively on the scale of loads.

The line AE will not, generally, be horizontal as shown in Fig. 3,
since its inclination is determined by the position of relative to MN.

The following table gives the maximum values of the bending
moment and the maximum deflections of beams for a few of the
standard examples frequently met with in practice.

TABLE I.

Method of
Sapporting.

Fixed at one end.

Supported at the
ends.

Fixed at the ends.
Fixed at the ends.

Method of Loading.

Maximum
Bending
Moment.

Loaded at the other.

Uniformly loaded with w
lbs. per in. run so that
wh = W.

Loaded in the middle.

Uniformly loaded with iv
lbs. per in. run so that
tvL= W.

Loaded in the middle.

Uniformly loaded with iv
lbs. per in. run so that
wL = W.

WL
2

WL
4

WL
12

Maximum
Deflection.

1 WL*

3 "EI

1 WL'

8 EI

1 W

48 EI

_5^WL8
384 EI

J_TO
192 EI

J_WL«
384 EI

The internal forces called into operation by the external forcee

MOTOR CAR ENGINEERING

hare al&o a moment about the neutral asis of the eeotion, which
is termed the " moment of reaistftnce." It can be shown • that if
M ia the bending moment in lbs.-inche8, I is the moment of
inertia of the cross section, / is the stress produced in the extreme
fibres at a distance y from the neutral axis, then

M=/i=/Z

where Z is the modulus of the section.
The neutral axis will pass through the centroid or centre of
gravity of the section in a material equally strong in tension and
compression.

Table II. shows the values of land Z for various cross-sections
of beams : —

TABLE IT.

Form of Section.

#1
©I

|L(JH'+ BW)
' S«e test-books on Applied Mechanies.

■i(D' + ^)

1 / BA'-taH 'v
leVHA-fta^

MATERIALS OP CONSTRUCTION 21

18. Shearing Force. — When a beam is loaded in any manner,
one of the conditions which must be falfilled for equilibrium is that
the algebraic sum of all the vertical forces, internal and external,
must be zero. If all the external forces acting upon the beam
are vertical, there is no horizontal component, and the algebraic
sum of all the external forces on one side of any section is the
" shearing force '' at that section.

Ill the beam shown in Fig. 2 the downward force at D has reactions
R and Rj at the points of support, and therefore the shearing force at
any section between A andD is Ri. Similarly, the shearing force at
any section between D and C is — R. For a beam loaded as shown in
Fig. 3, the reactions Ri and R,, have been previously determined. Then
the shearing force from A to B will be R, = W, + W, + W3 - R„
from B to C will be Rj - W, = W, + W, - R» from C to D will
be Ri - W, — Wj = W, — R, and from D to E will be = — R,.
These values have been plotted and are shown in the figure by the line
AFGHSCTUYWE. Negative shear is taken as meaning, that the
tendency of the forces acting is to cause the right hand portion of the
beam to move downwards relatively to the left hand portion.

We may also use the scale of loads shown in Fig. 3 for the determina-
tion of the shearing force diagram by drawing horizontal lines through
MNXQR. The line through X is the zero line AE, and AF » shearing
force from A to B = MX ■= Rp Shearing force from B to C ^= BH =
NX = MX - MN = Ri - Wi, and so on.

If curves of bending moment and of shearing force are drawn it will
be generally found that the bending moment will be zero where the
shearing force is a maximum, and that the shearing force is zero where
the bending moment is a maximum. It should also be noted that if a
beam is symmetrically loaded by two forces, the shearing force between
the points of loading is zero.

19. TorsioiL. — If one end of a bar is fixed and the other end is
acted upon by a tangential force, the bar will be twisted ; so that
if the bar be circular, a straight line drawn on the surface of the
bar parallel to its axis will form a helix, making the same angle
9 with the generating line of the cylinder throughout its length.
If N be the coefficient of rigidity, or the shear modulus of
elasticity and f, is the maximum stress produced in the ba *, then
f^ =: N f because 9 is a measure of the strain. Thus, a radial
line, I ins. distant from the plane from which the angle <p is

2^ MOTOE CAB ENGINEERING

measured will move through ^n angle 0, where = =^ in

circular measure or = — :r^ in degrees = the angle of torsion.

From below (Art. 20) T = ^/.d^ and/, = ^-^g^.
Substituting the value of/, in the equation

^-Nd

, ^ 2T X 16Z

we have =

and T =

32i

Shafts subject to pure torsion fail through shear, so that/ is a
shear stress and increases from zero at the centre of the shaft to
a maximum at the circumference.

20. Twisting Moment. — The twisting moment, or torque, on a
shaft, is the moment of a force acting at right angles to a radial
line through its centre perpendicular to the axis of the shaft.
If a force F lbs. acts at a radius B ins. from the axis of a
shaft, the twisting moment T, is FR Ibs.-ins. If the units are
kilogrammes and centimetres, then the torque is measured in
kilos. -cm.

The resistance of a solid circular shaft to torsion is ^r^/D*

— jc — j where D and d are the

external and internal diameters respectively. Equating this to
the twisting moment : —

The moment of resistance of a square shaft to torsion is given
by the expression 0*2088®/ where S is the length of the side of
the square.

The consideration of shafts subject to combined bending and
twisting is reserved till later.

21. Factor of Safety.— The factor of safety is tlie ratio between
the ultimate strengtli of the material and the actual stress

MATERIALS OF CONSTRUCTION 23

employed in the design of a part. In working out the design of
any piece of machinery the following questions have to be
considered when determining the permissible static stress : —

(a) The maximum load to which the part is subjected.

(b) The ratio between the elastic limit and the ultimate tensile

strength of the material.

or shear, or a combination of any of these,
(rf) The character of the load — whether steady, alternating, or

fluctuating, and the rate at which the load is applied.
(«) Any allowance that should be made for wear, possible defects in

the material, unknown or indeterminate straining actions, etc.

As regards (b) it is obviously essential that the stress to which
any part is subjected under working conditions must not exceed
the stress corresponding to the elastic limit of the material
employed, in order to prevent any permanent deformation from
taking place since this would directly conduce to failure. For
ordinary carbon steels the elastic limit is roughly about 0*6 of
the ultimate tensile strength ; but in many of the steels used in
automobile work, the ratio is as much as 0*9, and sometimes even
higher than this after being heat-treated. Hence it is necessary
to allow a factor of safety of at least 1*66 for the former and of I'l
for the latter from this consideration alone if the working stress
is deduced from the ultimate strength.

The nature of the induced stress must also receive attenliion in
arriving at a suitable factor of safety on account of the variation
in the stress at which fracture occurs under the three forms of
loading — tension, compression and shear — and because it not
infrequently happens that the only information available relates
to its tensile qualities. As has been stated in Art. 10 the
approximate value of the strength of steel in compression is 0*9
and in shear 0*8 of the tensile strength, and the factor of safety
required from other considerations should therefore be divided by
one or other of these values when obtaining the permissible
working stress in compression or shear from the tensile strength
data.

Regarding (d), the researches of Wohler and others have
clearly demonstrated that the failure of materials subject to either
alternating or fluctuating stress occurs at stresses far below the

24 MOTOE CAR ENGINEERING

elastic limit under static load, and special attention is devoted in
the succeeding article to the behaviour of materials when under
these forms of stress. The rate of loading is of importance,
because when a load is suddenly applied to an elastic material it
is caused to vibrate in precisely the same manner as would a
spring if similarly acted upon — the amplitude of the vibrations
being equally disposed on either side of the mean position corre-
sponding to the strain which would result from a dead load
of equal magnitude. The amount of the strain in either direc-
tion is, however, equal to that which would be caused by a steady
load, and hence the stress induced in the material, if the elastic
limit is not exceeded, will be twice that produced by an equal but
static load. In many cases, however, the load is not entirely
dynamic, but is, in part, gradually applied. For example, when
the inertia forces are negligible, the end thrust in a connecting
rod during the compression stroke rises gradually to its full value,
but the rate of increase in pressure upon the piston at ignition is
extremely high — the load from the latter being about three times
that from the former. Hence, the maximum compressive stress
in the rod will be seven-fourths of the stress that would be pro-
duced by the application of a steady load.

Considerations of wear, the possibility of the presence of
defects in either the material used or in the workmanship em-
ployed in the manufacture of any part, especially as regards the
former with cast metals and alloy steels, where lack of homogeneity
or a variation in the heat-treatment accorded may seriously impair
their tenacity ; together with unknown or indeterminate straining
actions, such as internal stress, irregular distribution of the load,
preignition, back-firing, etc., require that the stress employed in
the design should be reduced in order to eliminate all risk of failure
from any of these causes. The allowance that should be made
will vary according to circumstances, and will, to some extent, be
dependent upon the opinion of the designer as to what increase
in the factor of safety is desirable, but in any case it should be
fairly substantial, say, from 1'75 to 2'0 for materials which are
thoroughly reliable and from 2*0 to 2*25 for castings and some
alloy steels. It will be seen that these values will give the factor
of safety for steels to satisfy considerations (b) and (e) as rang-
ing from 2*9 to 2*5 — the higher value for the lower grades of
steel — and about 3'75 for castings under a steady load.

MATERIALS OF CONSTRUCTION 25

From the preceding it should be quite clear that the factor of
safety does not represent the margin of strength but rather the
liability to failure, because all parts should be made equally
strong. The necessity for working in this manner arises from
the fact that it is not generally possible to ascertain the breaking
load of all materials under the conditions which obtain under
actual working conditions.

22. Flnctoating and alternating stress : — The fatigue to which
materials are subject when under prolonged alternating pr
fluctuating stresses much below the ultimate tensile strength is
now more fully understood than formerly, owing to the extensive
research that has been carried out during recent years in this
particular direction ; but even at the present time the explanation
of the phenomena exhibited by materials under these forms of
stress is not altogether satisfactory, and several theories have
been advanced in regard to them, of which the following is one
that is now generally accepted. The elastic limit referred to in
Art. 10 is that which is obtained by means of a static test, and
is sometimes referred to as the " primitive elastic limit." This
elastic limit is, however, capable of being varied by straining and
is artificially raised by the operations incidental to manufacture;
but it has been shown by Bauschinger,^ and to a large extent
confirmed by later experimenters, that when a material is sub-
jected to prolonged alternating stresses, new elastic limits in
tension and compression are obtained, called the '' natural elastic
limits." These he regarded as the limits of stress under an in-
definite number of alternations, and they are lower than the primi-
tive elastic limit ; consequently, it is necessary to raise the factor
of safety to prevent them from being exceeded in practice.
Readers should study carefully the subject-matter of and the dis-
cussion on the papers referred to in the footnote to this page.

From the experiments made by Wohler,^ Bauschinger,* Stanton
and Bairstow,^ Arnold,® Reynolds and Smith * and others,^ it has
been shown that the limiting stress is more dependent upon the
range of stress than upon the maximum intensity of stress. As
regards the effect of speed, the rate at which alternations occur

* Unwinds ** The Testing of Materials of Construction."
« Proceedingi Inst. CHril Engineers, 1906, Vol. CLXVI.
■ Transactions, Inst. Natal Architects, 1908, Vol. L.

* Phil, Transactums, Royal Society, 1902.

* Proceedings Inst. Mechanical Engineers, 1911, No. 4.

26 MOTOR CAR ENGINEERING

has apparently but little influence in causing the failure of the
material, although Osborne Reynolds,^ found a tendency to
reduce the resistance offered by the material at speeds of from
1,300 to 2,000 alternations per minute. On the other hand, the
experiments conducted by Professor B. Hopkinson* show that at
speeds of 7,000 alternations per minute, the effect produced is in
a directly opposite direction. This he attributes * to a reduction
in the amount of the small slips that occur in th^ material when
the stress exceeds the elastic limit and, consequently, in the
damage done per cycle of strain. When the cycles are performed
sufficiently slowly, the same amount of deformation is produced
irrespective of the speed, but when the speed exceeds, say, 2,000
revolutions per minute, the material has not time to flow to the
full extent and hence the " cyclical permanent set " is reduced.

Attempts have been made to connect the limiting stress with
the elastic limit or the ultimate tensile strength, but so far they
have not proved very successful. The equation expressing Ferber's
relation * is probably most closely in accord with observed results.
• It is as follows : —

/max. = 2 + "^V^ — n A J3.

• ■

Where A is the range of stress, p the ultimate tensile strength
and n is a variable depending upon the nature of the material.
For a steady load A = and /max. = j> ; for a load fluctuat-
ing between a maximum value and zero, A = /max. =
2/) (Vft^ 4- 1 — w) and for an alternating load in which the com-
pressive stress equals the tensile stress A = 2/max. ^^^ /max.

= ^ . For an alternating load in which the ratio between the

tensile and compressive loads is as a; is to 1, A = (1 + a;)/

max.

and /"max. = 1 Vj)^ — up (1 + x)f. For a fluctuating load

where the ratio of maximum to minimum load is 1 to x,

A = (1 — x) /^,. and /max. = yqp"^ "^V^ — n|? (1 — x)f.

The value of n varies as has been previously stated, with the

* Phil. Trafisaci'wns, Jioyal Siwietyy 1902.

« I^rocepding* j4, Royal Society, Vol. LXXXVI.

* Ih'oceed'uigt Imt, Mechanical Engincerg^ 1911, No. 4.

* Uiiwin's "The Testing of Materials of Construction."

MATEHIALS Oi' CONSTRtJCTION

material employed. From the experiments carried out by Wohler,
the resalts of which are confirmed by later investigators, it is
concluded that n for ductile materials is about 1*5, while, for less
elastic qualities it approrimates to 2. Thus for mild steel of 26*6
tons ultimate tensile strength it is 1*58, for 62 tons Erupp axle
steel it is 1*83, for untempered spring steel of 67*6 tons it is 2*14
and for a 89-tons steel rail n = 2*0. It will be observed that the
value of n is not dependent upon the ultimate tensile strength of
the mat-erial but upon its ductility and toughness, and generally
it may be assumed that the greater the elongation, the smaller
the value of n.

The following table is given in order to illustrate the effect of
the method of loading and the variation in n upon the maximum
stress causing fracture after an indefinite number of alternations
of stress : —

TABLE III.

steady Load.

Load varying between
a Maximum and Zero.

Tensile and Coroprcsftive
Load equal.

(1)

(2)

(3)

(4)

1-5

0*605 p

0*838 p

1-6

0*574 p

0*813 p

1-7

0*544 p

0*294 p

1-8

0*518 p

0*278 p

1-9

0*494 p

0*263 p

0*472 p

0*250 p

0*452 p

0*238 p

2-2

0'4SSp

227 p

It is clear that if the factor of safety used for design of struc-
tures subject to a steady load to allow for the considerations
mentioned in Art. 21 (6) and (e) is 29 and that n = 1*8, then for
any part loaded as in col. 8 of table, the factor of safety should be
5*6, and if as in col. 4, 10*4.

From what has now been stated, it should be clear that in
selecting materials for use in parts which are subject to alternat-
ing or fluctuating loads, the ultimate tensile strength is not the
only quality to which attention must be paid, as a material
having a high breaking stress may require the use of such a

28 MOTOR CAR ENGINEERING

factor of safety in design as will nullify its advantage in this
respect over another metal that has a lower ultimate tensile
strength but a greater percentage, elongation and a higher elastic
limit.

23. Impact Tests. — In. selecting materials for use in ordinary
engineering work, it is usually sufficient to ascertain the ultimate
strength, the elongation, the reduction of area, and occasionally
the angle through which a piece of the material may be bent or
twisted when cold, as these indicate the physical qualities of
strength and ductility. But where the loads to which the material
will be subjected in use are of a dynamic character these static
tests can be advantageously supplemented by an impact test.
There are many forms of impact testing machines, but, in general,
the specimen is fractured either by a single blow or by a
succession of blows from a falling weight, the energy absorbed
during fracture being the measure of its ability to withstand a
suddenly applied load. ^

In order, however, that the results obtained for various
materials may be comparative, it is necessary for the tests to
be made in the same or an exactly similar machine. For
particulars of the machines used, and the manner in which the
test is carried out, the reader is referred to text-books on the
strength of materials.^

24. Hardness Tests. — Materials may also be subjected to another
form of test for the purpose of determining their degree of
hardness. This quality is desirable when the part must be
capable of resisting wear, at crankshaft journals and pins, for
instance, as once a good smooth surface is produced a journal will
last for a considerable period without perceptible decrease in size,
while the glass surface will conduce to a reduction of the fric-
tional losses. The test is also especially of service for determining
the carbon content of steels and the uniformity of temper and
the examination of the effects of the heat treatment or cold
working of steel.

Tests are carried out either by indentation or by scoring,
Brineirs ball-impression test being probably that which is the
more frequently employed. In the former an indentation is pro-
duced in the surface of the material by means of a hardened

1 See Unwin b ** Materials of Construction," or Morley's *' Strength of Materials."

MATERIALS OF CONSTRUCTION

I-

I I ^ •*»5 O US O O M5 Ol Ol rt •*»i^ O I Q lOO I

CZ2

1-4 eo

d
o

-a

C
e<

C3
O

■

a
S.

£^eo

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2S I |5§giSgS ISA* I 12 I |«5

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*P <e e< lo I f

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M I I M I

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lO lo o o

QOO
lO

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C9

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04

a
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t»*a 4* '2 '5

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• "S'2

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s i

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MOTOR CAR ENGINEERING

TABLE V.
Ultimate Tensile STRENaxHa, etc., of Don-febbous Allots.

Material.

■

Specific

Ultimate

TahaiIa

Elastic

Elongation

Reduction

^^^^'^^r^ra v^^v^S

Gravity.

Strength.

Limit.

on 2".

of Area.

Phosphor Bronze Co.

Tons per

Per cent.

Phosphor Bronze,

sq. in.

Chill cast bare — Cogwheel

brand ....

—

23-21

1495

3 in 8"

3-4

Rolled— Cogwheel brand

40-34

226

Willans & Robinson.

Cheaper grades of Phosphor ]

25-6
21-76

51-6
30

Bronze cast bj Eaton ia >

^^^

31-6

process

Guntmtal cast by Eatonia

process ....

20-0

Muntz Metal Co.

Manganese Bronze. \
Rolled Bar . 1

J" dia.
«"dia.

28-66
28-98

—

JhV^i'&BX^^A Jk^&VA ^ a *

If" dia.

23-73

—

27-5

—

A luminium Bronze 10°/o Al.—

Hot rolled

—

Cold drawn

—

M.A.eAUoy Bar 8%A1.

45 to 50

— .

25 to 35

—

„ „ Castings .

5 to 10

Vickep, Ltd.

Duralumin— Qujilitj A

2-8 about

260

13-35

Quality D

2-8 about

29 2

16-5

Sterling Metals Ltd.

Aluminium Alloy. . .

2 96

5to7

—

n M Special .

—

15-8

Muntz Metal Co.

Aluminium Alloy A.M.

2-99

13-33

No. 1 .

2-8

» 2 .

2-85

„ 3 .

2-9

100

—

» 4 .

3-0

120

„ 5 .

3-08

130

—

» 6 .

3-3

160

« 7 .

3-45

200

—

„ 8 .

2-75

Hot rolled and cold drawn,

90% Al. 10 % Zn.

— .

140

—

M.A. Alloy Castings,

95%AL .

2-7

7-5

^M^

2 to4

~"~"

steel punch or ball, the force producing the depression being pro-
vided either by a certain mass falling through a known height, or
by a definite static pressure. The depth, area, or volume of the
indentation caused by the punch or ball is then measured, and
from it the hardness factor may be determined.^ It is claimed
that there exists a relationship between the ultimate tensile

^ See Unwinds *^ Materials of Construction/' or Morley's '^ Strength of Materials."

MATERIALS OF CONSTRUCTION

TABLE VI.

Spegifioationb fob Ibon and Steel issued by The Amebican Society of

Automobile Exqineebs.

Specifi-
cation.
No.

Matmal.

Carbon.

Man-
ganese.

Phos-
phoru8.

Sul-
phur.

Chro-
mium.

Nickel.

Remarks.

1010

010 Carbon .

•05— 15

•80— 60

•046*

•05*

) For case harden-
) ing.

1020

0-20 Carbon

•15— 25

t«

1025

0-25 Carbon

•20— -30

•50-'80

—

] For heat treat-

1035

0*35 Carbcn

•30— 40

•1

—

..«.

ment.

1043

45 Carbon

•45— 50

• I

II.

_^_

1095

0^95 Carbon

•90— lO'V

•25— 50

t)4*

—

Springs.

1114

Screw Stock

•08— •20

•30— •SO

•12*

•06—12

—

1236

Steel Castings .

•30- 40

•50—80

•05*

•05»

—

•10- 30 Silicon.

231,';

•15 C. 3-5 Xi. .

•10— -20

•04*

•045*

— [3-25— 875

For case harden-

2320

•20 C. 3-5 Ni. .

•15- 25

—

t»

ing.
\ For case harden-
ing or heat

2330

•30 C. 3-5 Xi. .

•25- 35

•1

•045 •

—

1 y

treatment.

2335

•35 0. 3 5 Xi. .

•30— 40

—

f f

1 For boat treat-
\ nient.

2;i40

•40 C. 3-5 Ni. .

•35— -45

9 t

3J-20

•20 C. Ni. Cr. .

•15— 26

•45— •75 100—1 50

For case harden-

3125

•25 C. Ni. Cr. .

•20— -30

y J

ing or heat

3130

•30 C. Xi. Cr. .

•25— 35

) 1

treatment.

3135

•35 C. Xi. Cr. .

•80— 40

f f

1 For heat treat-

3140

■40C.Ni. Cr..

•86— 45

^ ment.

3220

•20 C. Medm. Ni. Cr.

•15— 25

•30—60

•04»

•20-1-25

1-50—2 00

/ For caxe harden-
\ ing.

3230
3240
3-250

•30 C. Medm. Ni. Cr.
•40 C. Ni. Cr. .
•50 C. Ni. Cr. .

•25— 85
•36— 45
•45— -55

II
It
II

II
II

II
•1
II

•90^1-25
II

91
II
99

1 For heat treat-
[ ment.

X33I5

•15 C. Ni. Cr. .

•10— 20

•10— -20

• 1

■60— •OS 2 •75— 3-25

3321)

•20 C. Ni. Cr. .

•15— 25

•30—60

r25-l-75

( For case hanlen-
1 ing.

X3S35

•35 C. Ni. Cr. .

•30- 40

•65— -75

•60— •95

2-75— 3-25

3340

•40 C. Ni. Cr. .

•35— 45

•30—60

■04»

•04 •

1 •25— 1-75

325-375

f For heat treat-
1 ment.

X8350

•35 C. Ni. Cr. .

•45— -55

•45—75

•60— ^95

2 •76-3-25

5120

20 C. Cr.

•15— 25

•25— ^50
•60— -80

•046*

-65— -85

—

Silicon M*
Silicon 15— -50.

514C»

•40 C. Cr.

•35— 45

•25—50
•60—80

• 1

— •

1 Silicon as 5120.

5165

•65 C. Cr.

•60— •SO

•25— 50
•60—80

•I

—

1 Silicon as 5120.

5195

•95 C. l-O Cr. .

•90—105

•20- 45

•03*

03*

•90— 110

—

51120-

1 20C. 10 Cr. .

110— 130

—

For ball and

b2ir,

■95 C. 1-20 Cr.

•90— 105

• I

110— 130

—_

roller bcaringfl.

521-20

120C. 120Cr.

110— 1-80

• 1

^—

\ 'V2\ Vanailium.

6120

•20C. Cr. V. .

•15— ^25

•60—80

•04*

70- 110

—

1 Case harden -
r ing or heat
) treatment.

6125

•25 C. Cr. V. .

•20— 30

•1

—

6130

■30 C. Cr. V. .

•25— 86

• 1

6135

•35 C. Cr. V. .

•30— -40

—

•12t Vanadium.

6140

•40 C. Cr. V. .

•85— 46

—

Heat treat-

6145

•45 C. Cr. V. .

•40— 60

•I

—

ment

6150

•50 C. Cr. V. .

•45— 66

—

6195

•95 C. Cr. V. .

•90—105

•20— 45

•03*

•90— 11

V 1 50-2 00 Sili-

9250

Silico manganese

•45— 65

•60— -80

•04*

•40*

^—

l con. Heat
j treatment.

296

Valve metals (No. 1)

—

96«

—

230

Valve meUla (No. 2)

•60*
ToUl.

150*

•04»

•04*

28—35

Remainder Iron.
^ Combined C. =

Grey iron castings .

80 — 85

•40--70

•60—10

•10*

-"•

> -40- 70 Sili-
} con 1-76— 2^25.

Malleable iron .

"~"

•30— 70

•20*

•06*

^^ "^

Silicon 10.*

* Not more than, f Not less than. Ni. Nickel, Cr. Chromium, V. Vanadium, C. Carbon.

► »

32 MOTOR CAR ENGINEERING

strength and the hardness factor suoh that the former may be
ascertained by multiplying the latter by an empirical constant,
but the variation in the numerical value of the constant, accord-
ing to the heat treatment it has undergone, would appear to
considerably limit its usefulness in this direction.

Materials.

25. Iron Ores. — Iron and steel, which are so largely used at the
present day in all classes of engineering work, are obtained from
certain substances called iron ores, which are compounds of iron
with oxygen, water, sulphur, and carbonic acid. The principal
ores of iron are magnetic iron ore, red hematite specular ore,
brown haematite, spathic iron ore, clay ironstone, and black-band
ore. These ores, with the exception of the red haematite and
magnetic, are broken up and subjected to a process of calcination
or roasting during which some of the moisture, some sulphur
and carbonic acid gas is driven off, the ore being thereby rendered
more porous and therefore more easily subject to the reactions
that take place in the blast furnace. The removal of a portion
of the sulphur is sometimes assisted by the use of a steam
jet, the hydrogen in the steam combining with the sulphur to
form sulphuretted hydrogen.

In order to reduce the iron ore it is smelted at a very high
temperature in a blast furnace, where coke is generally used as
the fuel because of its great strength to resist crushing and its
high rate of burning, and a blast is introduced near the bottom
in order to obtain a grj3ater heat. It is very important that a
uniformly high temperature should be employed in smelting,
iron ore, as great variations in the physical and chemical pro-
perties of the iron occur even when the temperature varies between
narrow limits. Limestone is generally employed as the fluxing
agent to increase the fluidity of the slag which results from its
combination with the ash and the acid earthy matter, etc., which is
always present in the ore in varying proportions. This slag floats
on the surface of the molten metal and is drawn off at the bottom
of the furnace. The flux used is always in excess of that required,
as it has a beneficial effect upon the metal by absorbing sulphur
contained in the ore and the fuel, and which is objectionable
since it produces " hot-shortness," that is, the iron is unwork-

MATERIALS OP CONSTRUCTION 88

able when hot. When commencing operations, the lower part
ol the furnace, known as boshes, is filled with a quantity of wood
and coke, and then covered by alternate layers of fuel and of ore
and flux — the quantity of the latter gradually increasing as it
nears the top until the full charge is attained. In about 16
hours after starting, the iron commences to flow, and successive
charges of fuel and of ore and flux are added as necessary to
maintain the level in the furnace as the fuel is burnt and the ore
is melted. In the vicinity of the tuyeres which convey the hot
blast into the furnace, the carbon in the fuel is burnt to carbon
mon-oxide which, passing through the successive layers of ore
and fuel, combines with the oxygen in the ore to form carbon di-
oxide. The amount of carbon mon-oxide present is, however,
always in excess of that actually required to completely reduce
the iron, so as to prevent any oxide of iron from remaining in the
metal, and hence there is a considerable quantity of this gas in
the gases leaving the blast furnace. As the ore passes downwards
through the furnace it is first reduced to iron in a more or less
viscous state by the combination of the oxygen in the ore with
the carbon from the fuel, but by the time it has passed the com-
bustion zone and reached the hearth it has become sufficiently
fluid through the absorption of carbon (up to about 4 or 5 per
cent.) to allow it to be run from the furnace through what is
termed the '' sow," from whence it is distributed by lateral
channels and cast into '* pigs/'

The pig-iron is now in a very impure state, and contains
sulphur, phosphorus, silicon, manganese, etc., while the carbon
is present both chemically combined and as graphite or free
carbon in varying proportions. The percentages of these two
forms of carbon in the metal determine the grade of iron to
which the pig belongs. The grading of the pig-iron is not, how-
ever, universally the same, as in some localities there are five and
in others seven grades of iron, but the lowest number is always a
grey iron, which is soft, while the highest number is a white iron
and is hard and brittle. One or more of the intermediate grades
is termed a mottled iron. These terms — grey, mottled and white
— are applied to the irons according to the character of the
fracture obtained from them. The formation of grey iron is
facilitated by the slow cooling of the molten metal, as then the
carbon separates out, whereas if quickly cooled a greater percen-

M.C.E. i>

MOTOR CAR ENGINEERING

tage remains in chemical combination with the iron. In the
grey irons from 0*8 to 0*06 per cent, of carbon is combined and
from 2'6 to 3*5 per cent, is free ; in the mottled, from 1'4 to 1*7
per cent, is combined and from 2*2 to 1*5 per cent, is free, and
in the white irons from 2*5 to 8*2 per cent, is chemically com-
bined and about 01 or less is free. Usually a mixture of the
greyer irons is used for foundry purposes, while the white irons
are converted into wrought iron. The constituents of the pig
will vary largely with the district and the country, but the follow-
ing table shows the results of a typical analysis of foundry

irons-

From
To

Combined
Carbon.

Graphitic
Carbon.

Silicon.

Phosphorus.

Sulphur.

015
0-80

3-5

2-8

3-0
2-4

1-2
1-0

0-6
1-0

Manganese.

02
010

26. Cast Iron. — The composition of the iron used for a casting
depends upon the relative importance attributed to wearing
qualities, hardness, strength, density, etc., and upon the intricacy,
thickness or extent of the casting, for to obtain perfectly sound
eastings it is imperative that it runs well in the mould. These
qualities can, to a large extent, be controlled by regulating the
quantity and condition of the carbon and the percentage of
metalloids present. It is necessary, therefore, to examine the
effects produced by the various constituents on the characteristics
of the metal.

Within ordinary limits, as the percentage of carbon in a com-
bined form increases, so does also the strength, hardness and
density of the casting, but the metal also becomes more brittle.
An increase in graphitic carbon has, however, directly opposite
effects, but it renders the metal more easily cast because of its
greater fluidity. Thin castings would tend to become harder
during casting on account of the high rate of cooling were it not
for the presence of a higher percentage of silicon to give greater
fluidity in the mould.

Silicon alone operates as a hardening agent, but since it also
acts upon the carbon by increasing the proportion in a graphitic
form and thus making the final product softer, its relative effect

MATERIALS OF CONSTRUCTION 35

depends upon the proportions of this element in the metal.
With the percentages that are usually present, however,— from
1 to 2 per cent. — it appears to have little effect upon the hard-
ness of the metal, but greatly assists in giving fluidity during
casting operations. Thus raising the silicon content will soften
a white iron.

Phosphorus also gives greater fluidity, and although often
regarded as an objectionable constituent, is not generally harmful
but beneficial if not more than, say, 1 per cent, is present, especi-
ally in very thin castings. It increases the hardness slightly,
whitens the iron and lessens the tendency to form blowholes by
giving a longer time for the escape of gases before the metal
solidifies, but it decreases the strength and causes the metal to
become ** cold-short."

Sulphur generally has a hardening tendency through its action
upon the combined carbon, which it helps to retain in the com-
bined form having solidification of the metal in casting ; but it
should not exceed 0*1 per cent., since it segregates in the metal,
forms blowholes and thus weakens the casting. It should be
noted, however, that the effect of raising the sulphur content
increases the strength for the metal. Casting is usually more
diificult on account of the more sluggish action of the metal, and
the percentage present generally increases with the combined
carbon and during remelting.

Manganese hardens cast iron by its action on the carbon, which
it tends to keep in the combined form, thus correcting the action
of silicon. It has been shown, however, that the addition of
manganese up to 0*5 per cent, to an iron containing 2 per cent,
of silicon has the effect of softening the iron ; but if higher
percentages of manganese are added, the hardening tendency is
at once apparent. Manganese apparently stabilises the carbide
of iron. It also reduces the quantity of sulphur by uniting with
it to form manganese sulphide, which may be slagged off, and
hence gives sounder castings, greater strength and fluidity.

Vanadium is sometimes added to cast iron in small quantities,
and is beneficial in that it appears to cleanse the iron from any
oxygen or nitrogen which may be present, as well as assisting to
keep the carbon in a combined form, thus raising the tensile
strength of the metal.

In the production of the cylinders of petrol engines^ the

D 2

MOTOR CAR ENGINEERING

following percentages will be found to give a very satisfactory
casting : —

Combined
Carbon.

Graplytic
Carbon.

Silicon.

Phosphorus.

Sulphur.

MangandKO.

About 0-6

2-8- 30

About 1-5

0-6 07

0075 0-2

10 1-5

The Frodair Iron and Steel Co. recommend the following
irons : —

Brand.

Total
Carbon.

Silicon.

Phosphorus.

Sulphur.

Manganese.

Frodair

Bearcliffe

Norrfield Foundry ...

3-2
3-5
3-8

11
1-0
20

1-10

0-3

003

0-75
012
0-03

1-3
10
1-0

The Frodair iron is a hard, bright, dense, close-grained
cylinder iron, and gives sharp castings. Bearcliffe may be used
for thicker cylinders when the metal is strong, tough and close-
grained. Norrfield Foundry iron is used principally for castings
other than cylinders and has an ultimate tensile strength of from
12 to 13 tons. A mixture of 50 per cent. Frodair, 30 per cent.
Norrfield and 20 per cent, scrap (that is, pig-iron once melted)
has an ultimate strength in tension of about 16 tons, while a bar
2" X 1" placed on supports 3 feet apart will carry a load of about
IJ tons.

The ultimate tensile strength of cast iron used for ordinary
work varies from 6 to 14 tons per square inch, while its compres-
sive strength ranges from 25 to 70 tons per square inch, and
therefore it is more suitable for use where great compressive
strength is desired. It is evident from the value of E given in
Table IV. that the elongation of cast iron is greater than that of
steel, but this is only true for very low stresses, and on
account of its extremely brittle nature, cast iron should not be
employed for parts which are subject to shock or impact.

The great facility with which it may be made to take any
shape is one of the reasons why it has such an extensive use
in all classes of engineering work and makes it very suitable for

MATERIALS OF CONSTRUCTION 87

cylinders, crank-cases, etc., which are often of intricate construc-
tion. The excellent wearing properties of this metal are
especially of advantage in the production of cylinder castings, as
a hard, polished skin is soon formed by the movement of the
piston which resists wear and has a low coefficient of friction.
Cast iron has occasionally been used for worm wheels with highly
satisfactory results as regards efficiency and durability.

In designing parts which are to be made of cast iron great
care should be taken that all abrupt changes of form are avoided,
corners should be well rounded and the mass of metal well dis-
tributed in order that the metal may not be thrown into a state
of internal stress in cooling due to unequal contraction. In
general this is easily arranged for, and should be observed even
where the castings are subsequently subjected to an annealing
process, as is often done in the case of large castings either
before machining or after the outer skin has been removed.

27. ICalleable Cast Iron is produced from cast iron by removing
some of the carbon. In the usual process the castings are first
made in the usual manner and then subjected to a heat treat-
ment in contact with red hematite, during which a portion of the
carbon in the outer skin is removed by combination with the oxygen
in the reducing agent, while some of the combined carbon is pre-
cipitated in the form of finely-divided graphite, thus giving a
casting with a malleable exterior resembling wrought iron, and a
core of brittle cast iron. In the '' black heart** process, used in
some parts of America, the carbon is not eliminated but during
the slow cooling which is a form of annealing, separates out
in patches. The strength of castings made by the latter method
is slightly less than those from the former. Castings generally
lose some portion of the sulphur present.

The depth to which the decarburisation extends depends upon
the time during which it undergoes the heat treatment and the size
of the casting. This varies from five to nine days. Such castings
may be bent and will withstand heavy blows without fracture.

The ultimate tensile strength of the material ranges between
16 and 21 tons per square inch and the elongation from 3 to 7 per
cent., although metal has been produced with a slightly increased
tensile strength and about 12 per cent, elongation. The bending
angle without fracture when cold varies between 45 degrees and
180 degrees.

MOTOR OAR ENGINEERING

TABLE VII.
Steels ubed in Motor Cab Conbtsuction.

Tensile Test.

Torsion Test in 1" diameter,
8" long.

Grade of Steel.

mate
ngth.

§
1.

imum
ss.

•

«
<

§«

hIj

»§

K o

Tons

Per

Tons

I'ons

Degrees.

persq.

per .sq.

cent.

per sq.

persq.

W T. Flather. Ltd.

in.

Special Axle. As rolled

47'86

34-74

27-6

60-8

16-6

39 7

1.226

Oil toughened

52-63

40-88

24-0

47-0

27-6

47-8

930

**Ubas:' As rolled .

34*52

2812

24-5

57-2

14-5

36-5

1,670

Quenched 875° C— cased jA|".
Double quenched— cased Jji" .

46-36

84-80

3-2

8-1

39-6

48-8

—

30-2

47-5

Heat treated ....

—

21-4

43-9

456

SX Nickel. As rolled .

44-27

29-07

31-5

53-8

16-5

850

1,400

Oil temi>ered .

83-48

80-18

16-0

43-4

36-4

56-2

798

Oil toughened .

402-12

90-87

140

42-3

—

5 Z Nickel. As rolled .

46-76

81-6

27-0

434

20-8

42-9

1,014

Oil tempered .

93-4

88*12

160

45-4

66-1

75-2

202

Oil toughened .

108-17

84-75

160

35-7

—

'*Nykrom." As rolled.

75-76

61-07

14-5

38-4

32-5

56-5

792

Heat treated .

94-08

83-42

20-6

860

61-2

86-5

100

Chrome yanadium. As rolled .

57-13

46-42

26-0

61-2

—

Heat treated

iaO'39

106-19

8-0

19-9

—

— _

25 X ^'ickel for Foim. As rolled .

47-33

24-93

470

67-8

—

Air hardening " Nykrom** Gear .

108-8

96-8

12-6

36-4

—

Vickers, Ltd.

Nickel Chrome. Heat treated

58-0

45-6

19-5

63-6

33-5

49-2

1,252

Guaranteed

500

40-0

200

■—

—

Case hardening Nickel. Soft

330

28-0

33-0

650

—

— _

J" bar quenched in boiling )

36-5

30-0

32*0

70-0

water fWim l,450o P. \

w «^

Ua# V

1 ** w

1" bar quenched in cold )
water from 1,450" F.

67-6

61-6

16-0

57-0

—

1" bar quenched in cold )
water from 1,450° F. j

81*6

65-6

150

51-0

—

C'lBC hardening Mill— core only .

35 to 40

22 to 25

33-0to30

70 to 60

—

TABLE VIII.
Stbkls used IK Motor Car Construction.

Maker's
liStter.

TetUonic
TND
TNDc

TNO
TNG
TNO

TAP
TAP
TAP

No. 3
No. 3

TNC3

TNC8

NUB
TSS

Grade of Steel.

Stfel Co. :—
Nickel Chrome
Nickel Chrome

Nickel Chrome
Nickel Chrome
Nickel Chrome

Nickel Chrome
Nickel Chrome
Nickel Chrame

Nickel
Nickel

Nickel Case
Hardening.
Nickel Case
Hardening
Mild Steel for
Case hardening

•

Tons

per

sq. in.

100

114

106

100

110

43.5

113

114

17-26

28-30

30-35

60-66

•

B
O

Reduction
of Area.

Per

cent.

26-36

40-60

about

10-14

a
o

Per
cent.

Air Hardened
Oil Hardened

Annealed
Air Hardened
Oil Hardened

Untreated
Treated

Normalized

Cased

Normalized

Normalised

For what puriK>8e
Employed.

: Worms and shafts, dogs,

1 sliding gears.

, Transm ission shafts,

^ light connecting rods,
steering levers and
other highly stressed
parts.

f Propeller gears, dogs,
] driving shafts.

Live axles, shafts,
highly-Rtressed traits
and studs, connecting
rods, levers.
/ Camshafts,worms,cupft,
'I cones, bolts, gears gud •
^ geon pins.

{Gears, differentials,
shafts, etc., ball races
for light cars.
J Springs for motor omni-
1 buses, motor lorries.etc.

MATERIALS OF CONSTRUCTION

TABLE VUL—eontinued.

Maker's
Letter.

Qraile of Steel.

Observed
Dimensions.

Elastic
T.imit.

Ultimate

Tensile

Strength.

•

Reduction
of Area.

For what Purpose
Employed.

Tons

per

Per

sq. in.

cent.

PaldiSU

d Works:—

O-fiW"

CN'8

Chrome nickel

dia.x4*

Crankshafts and shafts
- sul^eeted to bending
and twisting.

TB03

Ditto .

AUTO

Auto ....

CN8
TBOS
AUTO

Chrome nickel
Ditto .
Auto ....

••
M
•t

42
29

50
48
45

27
24
23

66
66
60

. Axles, steering leverSt

1 connecting rods and

Darts subjected to

bending and shock.

V Axles, steering gear,

TT31I

Nickel annealed .

shaftSt leverst con-

W5W

Cast— annealed

«•

22-5

48-6

. necting rods, etc.

W6H

Cast— annealed

38-0

Steel must not be

W6W

Cast— annealed

heat-treated in any
' way.

Nr25

25% nickel .

»i

22-5

41-5

) For TaWes of very hot
f running engines.

TT5M

5% ditto .

25-5

38*0

For valves of well-
cooled engines.

TY3M

3% ditto .

24-5

TEl

TT8W

VAB

Chrome nickel annealed

case hardened
Kickel— annealed .

case hardened
Auto— annealed .

case hardened

t*
**
*•
It
ft
tt

70
23-5
32
17
25

51
83
32
41-5
27
38

24
18
86
29
87
28

56
50
6&
55
55
55

For case hardening.
Camshafts, gear
- wheels, live axles,
steering parts, gud-
geon pins, etc.

CNL

Chrome nickel tin
hardened

115

Gearwheels, pins,
■ cranks and other
shafts.

E3L

Special gear-
annealed

For hardening without

casing. Qear and

hardened .

. other wheels, square

tempered .

shafts, etc., in heavy
work.

^ahlwer

: Baker :—

KO30

Nickel-

annealed .

4" long

22-5

80-9

80-8

66-2

hardened .

48*0

58-0

12-8

49-0

guaranteed

44-0

55-0

12-0

—

Steering parts, axles,

KO40

Nickel-

- and gear wheels. For

annealed .

29-3

88-7

22-9

68-6

use case hardened.

hardened .

58-4

84-5

16-5

82-0

guaranteed

64*0

78*0

120

—

NOOl

Nickel chrome-

N Oaiu* whsftlji Iavapa

annealed .
hardened .
guaranteed

ft
tt
It

26-4
47-6
45-0

89-2
64-7
57-0

21-5
12-8
10-0

61-3
88-&

1 sliding shafts, rollers,
1 and cams. For use
J case hardened.

NCOS

Nickel chxome—

annealed .

41-4

48-7

17-5

62-6

hardened .

63-2

77-7

10-7

44-3

guaranteed

600

760

100

—

NOfiS

Nickel chrome —

annealed .

51-4

17-2

62-6

Gear wheels, steering

hardened .

80-3

91-4

10-4

46-0

>. gears, etc., in heavy

guaranteed

8-0

—

work. For use case

NWO

Nickel tungsten-

hardened.

annealed .

39-1

511

18-0

65-7

hardened .

75-4

850

9.4

60-0

guaranteed

730

82*0

^^"

MOTOR CAR ENGINEERING

For ^hat Purpose
Employed.

Dumbirons, steer! Dg

" levers, axles, etc.

For case hardening.

Connecting rods,
IcTcrs, etc.

Steering gear, sprocket
' wheels, etc.

•

^ As R. H. B.

Nickel chrome steel.
. For oil tempering,

shafting, etc.
Nickel chrome steel.
For air hardening.
I Gears, transmission
shafts, connecting
rods, etc.

r- ■ > - > f V- ■ ■•

<" - -v

Hardness
Number.

9)^ CO*^ <0 tOto 0O'^0OtCt<«

Oi"^ Oi^ "O »OQO CO-^WOOO

■^ !-!•»*« i-l N SO i-l -^ CS| N CO

QO "^ 94
94 -* -*
94 tf lO

Plain
Bars.

ft. lbs.
per cm*.

416-511
511-620

255-306
306-357

292-366

511-625
416-511
204-306

■

Nickel
Bars.

204-306
306-416

109-204
153-255

153-255

253-306
146-219

128-204
80-124

Sir

Number

of
Twists.

Q «o p o
« »o "^Heo to -ir sfi ^

1 1 Mil

00 CO CO G4 «0

ift to lO

• • •

CO C<l o

.2-6 —30
025—0-5

Maxi-
mum
Stress.

Tons

per

sq. in.

29-32

32-35

38-41
45-47

38-41

41-44
64-57
66-69

47-50
94-97

Elastic
Limit.

Tons

per

sq. in.

9-11

12-14

15-17
20-22

22-25

22-25
39-43
4447

29-32
72-75

Tensile Test.

•

Con-
traction
of Area.

Per
cent

OO »0 »00»00«COiO OOtO

t«-QO «Ct«- <0t«--^»0iNl>»<0 ,t*t*«0
• 1 II 1 1 1 t 1 1 1 1 t 1 1

lOiO OtO QOiOOiOOiOO 1*0*0

«OC« coco lOCO^V'-^MCOCO cotoio

40-58

30-35

8-10

Elon-
gation
in 4*

Per-
cent

OeO e* *0 C4C4Q09«e4OQ0 C«94iO

'^H''** coco ,COCOt-^C<I^N'-i l-i©«'-^
II 1 1 1 1 i i 1 i 1 I 1 94 1 1

kOQO 00^ iaoooiOO»ootco4 'ooaoo

COCO ©4 CO M C^ .-H ^ ^ -^ ^^^

15-18
8-10
6-8

Elastic
Limit

Tons per
sq. in.

cOQO O"!** ^t-^cviicaoQoao to a to

i^i-4 |i^G4 \ Vi C9 CO efi t^ Vi '^ icotooo

lll«llllilll«llli

COiO 'coo '«"*f<QOC^OtO-^ 'M»OCO

^^ ^ e^ 04 94 C4 CO »« CO ^ OO -^ 00

44-48

108

114-121

Ultimate
Strength.

Tons per
sq. in.

lOOO 94»0 ooeo^"^so»-^o i-Ht^O

G49) COCO CO-^tOiOOOtOCO |tOlOi-N
II II • 1 I 1 • • 1 1 • 1 i

•^lO Qoeo iOo>ao94coaot» 'QO'<«4ao
e« ©4 cq 30 CO CO '^ »o i> "* lO ^ lO A

57-60

117

121-127

..J
o

Natural state
Tempe:ed . .
Case hardened
Natural state
Tempered . .
Case hardened
Natural state
Tempered . .
Natural state
Tempered . .
Oil hardened .
Annealed . .
Tempered . .
Case hardened
Annealed . .
Tempered . .
Oil hardened .

Annealed . .
Air hardened .
Oil hardened .

•

fij m W Q d Q
d W Q > Jzi W
» P4 6 tzi pq d

•
•

MATERIALS OF CONSTRUCTION

TABLE IXa.
Steels used in Motor-cab Construction.

Brand.

C 9

Deg.C

St/ihlucerk
NC02
(Nickel
C'hrome)

(Sickel
('hrome)
NOA
( Nickel
Chrome)
NCAIO
(Nickel
Chrome)
NCAV
(.Vickel
Chrome-
Vanadium)
NC04
(Nickel
Chrome)
F.S

Tons

per

8q. in.

5«5

Tons

per

sq. in.

o —

Becker^ A. G.

51)0 o7

550 45

600 38

500 60

550 64

600 47

500 41

600 H8

650 35

500 62

600 50

700 43

600 57

650 50

720 —

760 —

600 99-6

650 86-6

63
50
45
65
58
54
60
45
41
70
57
50
60

100
104
91

Per

cent.

8
12
16
10
12
14
12
15
18
10
14
18
10

7-8
90

•

t? fi

o -

-mm t^

ffl?

3>:

Contract
of Arci

Impact T
ft. Iba. per

Hardne
Numbe

Par

cent.

304

145

244

200

221

115

240

145

285

180

250

145

238

170

212

200

191

—

115

270

145

227

100

290

110

275

505

512

—

For what Purpoae
Employed.

Engine shafts.
Front and rear axles.

\ Parts subject to torsion and
i bending.

Connecting rods, axles, etc.

Axles, shafting, etc.
( Axles, connecting rods,
steering gear, etc.

Similar to NCA.

Gear wheels, cams, rollers,
etc.

Gear wheels. Air harden-
ing.

_ / Springs.

28. Wrouglit Iron. — Wrought iron is obtained from cast iron
or pig-iron by removing practically all the carbon in a reverbera-
tory furnace. This is effected by heating the metal in such a
manner that only the hot gases flow over the surface of the metal
— the carbon is oxidised passing away as COa, and the greater
part of the impurities are eliminated during the process. White
pig-iron mixed with iron scrap is generally used, as the former
does not become so fluid when heated, and while in this plastic state
it is worked or puddled to facilitate the removal of the carbon,
manganese, sulphur, phosphorus, silicon, etc. As puddling
proceeds and the iron becomes purer, it forms into spongy
lumps of iron and slag, which are removed while in a plastic
condition, hammered to remove the slag, and then rolled into
bars. The removal of the slag is not, however, entirely effected

42 MOTOR CAR ENGINEERING

even after rolling and fagotting, so that about 1*5 per cent,
remains distributed between the fibres of the metal.

To produce the various grades of wrought iron, these bars are
cut up, piled or fagotted, re-heated and rolled or hammered again,
each series of operations improving the quality of the material
and resulting in the irons to which the commercial terms Mer-
chant Bar, Best Bar, Best Best Bar and Treble Best Bar are
apphed.

The percentage of carbon, which is combined, may amount to
0*6 per cent, or even slightly higher, while phosphorus, silicon
and sulphur are usually also present in very small propor-
tions.

29. Steel. — The term " steel " embraces materials that are
widely different in their mechanical properties, as is evidenced
by a perusal of Tables IV. and VII. to IXa. on pages 29 and 38 — 41.
The differences are principally due to variations in their chemical
composition and the heat treatment to which they are subjected,
small variations in which having marked effects upon the results
obtained from the finished material.

As has been previously stated, wrought iron contains up to
about 0*6 per cent, of carbon and cast iron from 1*9 to a maxi-
mum of 4*6 per cent. ; steel, however, may include a material which
has almost as low a percentage of carbon as wrought iron or as
high a percentage as cast iron.

In the very mild steels the carbon content ranges from 0*26 to
0*4 per cent., and in steel used for forgings it varies between 0*3
and 1*6 per cent., the harder steels containing from 1*2 to nearly
2*0 per cent, of carbon. Though intermediate, however, in this
respect, it is neither intermediate in strength nor in ductility,
many of the modern alloy steels having an elongation in excess of
that found in the best wrought iron (compare Tables IV. and VII.).

Steel may be made either from wrought iron or from cast iron.

In the Bessemer acid process, grey pig-iron is first melted in
a cupola and run into a converter. An air blast is then sent
through the molten metal for about twenty minutes to purify and
decarburise the iron, the oxygen in the air combining with and
eliminating the silicon, a little phoEphorus, carbon, manganese,
sulphur and carbon. At the commencement of the " blow " the
air attacks the silicon and manganese, causing great heat to be
generated and producing little observable effect, the resulting

MATERIALS OP CONSTRUCTION 48

silica and oxide of manganese remaining in the converter as slag.
The carbon is then acted upon by the air, producing CO. As the
heat is sufficient to prevent GO from remaining stable in
the body of the metal, flames of burning CO rise from its
surface. The end of the decarburisation is denoted by the
cessation of this intense flame, at which the blast is stopped
and spiegeleisen or ferro-manganese added to impart the required
percentage of carbon and to remove the oxides of iron formed
during the *' boil/' The blast is then sometimes continued for
a few seconds to assist the complete admixture of the carbon
with the iron and enable a more homogeneous metal to be
obtained. Owing to the difficulties experienced with the removal
of the sulphur and the phosphorus, only pig-iron produced from
oies which are very free from these two elements can thus be
utilised in the manufacture of steel.

In order to enable the inferior ores containing higher percent-
ages of phosphorus to be used, the Thamas-Oilchrist or Bessemer
basic process is employed. The character of the steel produced
depends largely upon its carbon content, and since carbon has a
greater affinity for oxygen than has phosphorus, the phosphoric
acid loses its oxygen by combination with the carbon, the phos-
phorus uniting with the oxide of iron, and is not therefore
eliminated. Further, if lime is added as a flux, since it combines
more readily with silica than with phosphorus, the siliceous lining
(ganister) of the converter will prevent the removal of the phos-
phoric acid. Thomas and Gilchrist overcame this difficulty by
employing magnesite or dolomite as a lining, as this is capable of
resisting very high temperatures, being unaffected by the lime.
With the Bessemer process, the high temperature obtained was
largely due to the presence of silicon in the pig ; but when using
the lower grades of iron the percentage of silicon is greatly
reduced and that of phosphorus is increased, consequently, as the
temperature must be maintained in order to keep the metal fluid,
the necessary heat must be supplied by the phosphorus, which
may therefore be present in greater cniantities with beneficial
results. The presence of sulphur, however, in the pig precludes
the use of very inferior ores, as sometimes only about one-half
the sulphur is expelled during the process.

The actual operations in the converter are similar to those
carried out with the ordinary Bessemer process except that blow-

44 MOTOR CAR ENGINEERING

ing is prolonged for a short time after the decarburisation of the
metal has been effected, as it is not until the carbon has been
removed that the phosphorus is eliminated.

In the Siemens-Martin or Acid Open hearth process pig-iron
and scrap are used, and in the Siemens process pig-iron and
hematite iron ores. With the former the pig-iron and scrap are
melted together in a regenqrative furnace having a siliceous
lining to the hearth, with limestone as a flux, and the carbon is
eliminated by the oxidising action of the hot gases, while in the
latter the decarburisation is almost wholly effected by the iron
ores, and a large proportion of slag is produced. At the present
time, however, the process is a combination of the two, in that
pig-iron, scrap and ore are used. Fig-iron and scrap are first
placed on the hearth, and when melted, this hematite iron ore is
gradually added to oxidise the carbon, forming carbon monoxide
and converting the silicon to silica. Very little sulphur or
phosphorus is eliminated during the process, and hence it is
essential for these elements to exist in but small proportions in
the pig. When the molten metal is practically decarburised the
required percentage of carbon is imparted by the addition of
spiegeleisen or ferro-manganese, which are alloys very rich in
carbon, the former containing not more than 20 per cent, of
manganese and the latter up to 80 per cent. The latter may be
added either in the furnace or as the metal flows into the ladle.
A small percentage of manganese is desirable, as it is found
to improve the quality of the steel by removing the oxides of iron
and increasing its ductility.

Steel is also made by the basic open hearth process. . The
furnace used is similar to that employed in the acid process
excepting that the siliceous or acid lining is replaced by one
composed of dolomite, thereby enabling high phosphoric pig to be
converted into steel, as in the basic Bessemer process. The
removal of the phosphorus and the carbon is facilitated by the
addition of the iron ore after melting down the pig and scrap, as
in the acid process. The wear of the furnace with the basic
lining is much greater than with an acid lining, as although
limestone is spread over the hearth before the introduction of
the charge, some fluxing away of the lining always occurs.

The open hearth processes possess the great advantage that
the molten metal can be kept in a fluid condition on the hearth

MATERIALS OF CONSTRUCTION 45

until the desired carbon content is obtained, and hence the manu-
facture is under better control than in the Bessemer processes,
which are used principally in the manufacture of low-carbon
steels.

The molten steel resulting from these processes is run into
ladles and cast in the form of ingots. When it is desired to
obtain a steel for forging purposes, these ingots are piled or
f agotted, placed in soaking pits to thoroughly heat, them up and
hammered or rolled to produce blooms or bars — the hammering
and rolling improving the quality of the steel. For the produc-
tion of steel castings, the ingots may be melted directly without
any preliminary rolling, but it is usual to add a small proportion
of silicon to the molten metal in the furnace to facilitate casting,
if such is intended.

The ultimate tensile strength of these carbon steels varies
greatly, increasing with percentage of carbon present, and it is
important to note that as the percentage of carbon increases,
so does also the difficulty experienced in welding and forging, so
that about 1*5 per cent, represents the limit up to which it may
be present in material for parts that have to be welded together.
During this increase, however, the capability of being hardened
and tempered develops, 0*6 per cent, being about the lowest limit
at which this property is evident.

SO. Alloy Steels. — Steel has such an extensive use in all
classes of engineering work on account of its high tensile strength
and elasticity and the facility with which it may be forged or
pressed into any shape. But in no class of work are these quali-
ties so necessary as in automobile construction where the loads to
which the various component parts are subjected are of an
exceptionally severe nature, and where lightness is of such great
importance, not only because of the considerations mentioned
in Art. 248, Vol. I., but also because of the magnitude of the inertia
forces at high engine or car speeds. For these reasons, pressed
steel pistons, H-section connecting rods, pressed steel framing
and axle casings, etc., have been introduced into the modern
vehicle, but have only been rendered possible because of the
excellent grades of steel which are now available for the use of
the automobile engineer.

An inspection of Tables VII. to IXa. will, however, show that,

46 MOTOR CAR ENGINEERING

in order to obtain the full benefits which may accrue from the
use of these steels, it is necessary to subject them to suitable
heat treatments. These vary greatly in character, as they depend
largely upon the chemical composition of the material and the
qualities it is desirable that the finished steel should possess,
and hence it is not possible to specify a heat treatment as
suitable for all grades of steel ^ ; but, in general, it is necessary to
heat the material above a certain critical temperature (from
700** to 850° C. according to its composition), and then quickly
cool it down in water, oil or a blast of air. This has the effect
of fully hardening the steel, in which state it has a high elastic
limit and ultimate tensile strength, but is too brittle for most
purposes, and hence it is necessary to temper it at such a
temperature as will bring out the desired qualities. The degree
of hardness obtained depends upon the rapidity of cooling
through the critical range of temperature, and therefore upon the
nature and the volume of the quenching medium. Water has a
greater conductivity than oil, and this may be increased by the
addition of salt to the water, and hence, will give a greater hard-
ness than will oil. The temperature of the cooling fluid will
also affect the degree of hardness, because the colder the water,
the higher the rate of cooling. In tempering springs, baths of
lead or lead- tin alloys are often used. The effects of tempering
are exhibited in Table IXa. p. 41, from which it will be observed
that as the tempering temperature rises, the ultimate tensile
strength, elastic limit and hardness decrease, the two former
generally approaching each other, while at the same time the
elongation, contraction of area and resistance to impact are
increased, and hence the material becomes tougher. The
critical temperature, or point of recalescence, above referred to
is the temperature at which a change in the condition of the
carbon in the steel takes place. In ordinary carbon steels the
change takes place very quickly, and hence the necessity of rapid
cooling, but the effect of the addition of chromium, tungsten,
vanadium, etc., is to considerably retard this change, so that with
some kinds of steel — called air-hardening steels — it is unnecessary
to quench them, since they are self -hardening. These are heated
to slightly above the critical temperature and then allowed to

^ A number of forms of heat- treatment have been standardised by the American
Society of Automobile Engineers for use with various grades of steeL

MATERIALS OF CONSTRUCTION 47

cool slowly in air. Such steels are capable of being annealed,
and can be obtained in varying degrees of hardness for
machining. The tenacity of some self-hardening steels after air
hardening is raised to over 120 tons per square inch. Steels
hardened in oil have a greater percentage elongation, contraction
of area and resistance to impact than when quenched in water,
and therefore oil is superior to water as a quenching medium
for parts that are subject to shock or to varying stress. It is
sometimes remarked that the results obtained from tests carried
out on heat-treated specimens afford little indication of those
possible of attainment in ordinary practice, and this may be
true regarding very large forgings, but it is doubtful if it is, to
any appreciable extent, applicable to the sizes of forgings used in
automobile work.

The principal alloy steels are those containing nickel, chrome,
vanadium, nickel and chrome and chrome and vanadium, all of
which, it should be noted, have a proportionately high elastic limit
even though the percentage elongation is generally reduced after
treatment.

Fickel and nickel chrome steels are extensively employed in
automobile work, and are obtained by the addition of varying
percentages of nickel or chromium during the processes of
manufacture which have the effect of raising the elastic limit
and hardness factor without impairing the toughness of the
material, but rather increasing it.

Generally the nickel steels contain from 8 to 5 per cent, of
nickel, although higher percentages, up to 10 or 12, are occasionally
employed, but it is unusual to exceed the latter figure except for
very special purposes, such as for valves from 25 to 30 per cent.,
since while the tenacity increases, the elongation, etc., diminishes
very rapidly until about 28 per cent, is attained, and then the
strength decreases and the ductility increases. The carbon
content varies between 0'2 and 0'9 per cent., while manganese is
also present to the extent of from 0*8 to 0*8 per cent. This steel
is exceedingly difficult to weld up and requires expert and careful
treatment in forging and pressing into shape. The nickel in the
steel for valves is for the purpose of obtaining greater ductility
and because it possesses remarkable properties in resisting the
corrosive action of the hot gases in the cylinder. The main
effect of chromium seems to be in the direction of hardening the

48 MOTOR CAR ENGINEERING

steel and developing certain self -hardening properties, and when
used in conjunction with nickel it produces a steel that is widely
used in moderncarsin parts that are subjected to alternating or
varying stress and shock. The percentage of chromium present
varies from 0*6 to about 8'6 or slightly higher in some instances,
but more usually from 0*6 to 1*5. Messrs. Vickers, Ltd., quote
figures which illustrate the ductility of their nickel-chrome steel
under torsion, for whereas the elastic shearing stress relative to
ordinary axle steel is as 1*95 to 1, the ultimate angle of twist at
fracture is only as 0"89 to 1. Such steel is therefore suitable
for crankshafts, camshafts, propeller shafts and axles, and may
be used with advantage for connecting rods. These steels soon
take a smooth hard skin at the journals which is conducive to
long life. In some instances the chassis frames are made of
nickel chrome steel ; but these are very difficult and expensive to
manufacture, owing to the elaborate processes through which it
passes, and the costly nature of the dies, etc.

Both nickel and nickel chrome steels are used for gear wheels,
but in this case require to have a hardened surface in order to
resist wear, and prevent noise occurring from imperfect action.
This may be produced either by oil tempering or by case
hardening (see Art. 82), but distortion is then almost inevit-
able, and a somewhat better method is to employ self-hardening
steels above referred to.

VaiLBdiiun steels were, at one time, viewed with suspicion, but
as the result of a considerable amount of research^ that has
been engaged in, it is now realised that they form a group of
steels, especially when alloyed in combination with chromium,
that are unequalled for their resistance to fracture under
fluctuating and dynamic loads.

Vanadium is a most powerful metal to alloy with steel, as the
addition of only 0*1 per cent, will increase^ the ultimate tensile
strength by over 80 per cent., and the elastic limit by over 40
per cent., producing a steel that is exceedingly hard and ductile,
so that vanadium steel can now compete on very favourable
terms with nickel or nickel chrome steel, containing 4 or 5 per
cent, of nickel, notwithstanding, the high price of vanadium.
This improvement is largely produced by reason of its scavenging
effect upon any oxides contained in the metal and from its effect

1 See Proceedings Irut, Mech, Engineers^ 1904.

MATERIALS OF CONSTRUCTION 49

upon the carbon , which it prevents from exhibiting any tendency
to segregate. In general, it is usually used in conjunction with
chromium, but sometimes with nickel and chromium, where it is
added in the form of a ferro-vanadium, which contains about
25 per cent, of the alloy, which, in a pure state is extremely
difficult to melt.

The percentage of vanadium present varies from 0*12 to 0*2,
the former being used when the steel is case-hardened, while
the latter is usually alloyed with about 0*8 to 1*0 per cent, of
chromium or from 0*5 to 0*8 of chromium and from 1*0 to 1*5
per cent, of nickel, the carbon varying between 0*12 and 0*15
for the lower vanadium content and from 0*25 to 0*5 for the
higher. Examples of these steels are given in Tables YII. and
IX. on pp. 88 and 40.

31. Aimealing. — Annealing is one of the most important
factors in the treatment of steels and it has the effect of bringing
the material into a state of greater molecular uniformity, thereby
removing internal stress due to unequal cooling or produced by
cold working, rolling or drawing which harden the metal in a
way which is quite different from the hardening produced by
quenching ; while at the same time, it renders the material
sufficiently soft to enable it to be readily machined. It is
especially required in parts that have been subjected to pressing
operations and die forging because the plastic strains which the
metal undergoes in different directions produces lines of cleavage
along which the material has a tendency to fail.

During the operation it is very essential to subject the
material to the requisite temperature for a sufficiently long time
in order to allow the heat to thoroughly soak into the metal.
Annealing should always be carried out in boxes from which air
is excluded, so as to avoid any possibility of the oxidisation of the
carbon, especially with high carbon steels.

Annealed specimens have not so great a resistance to shock or
impact despite their increased elongation and contraction of area,
because of the reduction which takes place in the elastic limit of
the material.

82. Cafle-hardening. — Case-hardening is often resorted to where
the material is subjected to hard wear (such as with cams and
gear teeth), and also to shock, which necessitates a tough, fibrous
core. Both ordinary low carbon and nickel or nickel chrome

M.C.E. 13

50 MOTOR CAR ENGINEERING

steels containing a low percentage of carbon, say, about 0*15 per
cent., may undergo this process, which is effected by the addition
of a percentage of carbon to the exterior of the metal. The
portion of the metal to be carburised is heated to a cherry red,
preferably in a closed box, in contact with the nitrogenous
mixtures, of which there are many in common use, for several
hours — the duration of heating depending upon the depth to
which carburisation is desired — and then allowed to cool slowly.
Subsequent heating in a gas muffle and sudden cooling hardens
the high carbon exterior; but in some cases this heating and
previous slow cooling are not carried out, the chilling being
effected on withdrawal from- the casing compound. Messrs.
Yickers recommend the following method for casing their mild
steel. After the steel has been heated at a temperature of 950^ G.
in a suitable mixture for several hours it is completely cooled off,
and is hardened in one of two ways. In the first method it is
heated first to about 900° C, and quenched in cold water, then
reheated to about 780° C, and again quenched in cold water. In
the second method the steel is heated only once to between 850°
and 900° C, and quenched in cold water. Either method will
give a fibrous core, but the first gives the better result. The
tensile strength, etc., of the core of a case-hardened mild steel
bar I inch diameter are recorded in Table VII., p. 88.

For case-hardening their G.H.N, steel for gear wheels a depth
of ^ inch is sufficient, and may be obtained by heating in the
casing mixture at 950° G. for from two to three hours, and
then permitting the box containing the article to cool slowly. To
harden the now highly carburised exterior two quite different
results may be obtained according to the temperature of the water
in which the article is quenched after reheating, as is indicated
by the results shown in Table VII. The effect of the diameter of
the bar upon the resulting mechanical properties is also clearly
established. Quenching in actually boiling water gives a rather
softer skin and more ductile core than does quenching in cold
water. When using the latter, the second heating should be
carried to from 760° to 790° G., and before plunging into
water the article should be allowed to cool a few degrees in the
air, but the actual temperatures and the treatment given depend
entirely upon the composition of the steel, and these particulars
only apply to Vickers steel.

MATERIALS OF CONSTRUCTION 61

Bat since distortion is almost inevitable, and this is often
accompanied by the development of surface cracks, which are not
removed by the subsequent grinding and polishing, Messrs.
Yickers have introduced their patented surface-hardening process
for gears made of nickel chrome steel. In this method the flame
from an oxy-acetylene blowpipe is rapidly drawn across the faces of
the teeth of gear wheels, raising the temperature of the surface of
the teeth for a depth of from ^ inch to ^ inch as desired. As the
flame passes along an equally rapid fall of temperature takes place
by the conduction of heat to the remainder of the tooth, resulting
in the production of a dead hard skin free from any distortion.

33. Bronzes. — These strictly consist of alloys of copper and tin,
but sometimes one or more other substances are added. Of gun-
metal there are many grades, which are used for a variety of pur-
poses, principally, however, for small castings, and in its harder
form, for certain bearings, the great characteristic of the metal
being brittleness. The ultimate tensile strength of gunmetal
ranges from 8 to 16 tons per square inch, from which it may be
concluded that the composition varies considerably. Ordinary
gunmetal contains from 86 to 88 per cent, of copper, 10 to 12 of
tin, and 2 to 4 of zinc ; soft gunmetal about 92 per cent, of copper
and 8 per cent, of tin ; while a hard bearing metal may, have 84 per
cent, of copper and 16 per cent, of tin. Some founders partially
replace the tin by antimony in small coatings with satisfactory
results. The A.SA.E. specification for red brass is 85 per cent,
copper, 5 per cent, tin, 5 per cent, lead, and 5 per cent. zinc.

PhoBphor bronze is largely used for bearings, worm wheels,
clutch plates, etc., where sliding contact takes place, because of
its excellent wearing properties under this condition, together
with a fair measure of strength and elasticity, especially after
forging or rolling and annealing. As cast it has a good percentage
elongation, which is reduced somewhat by rolling, but may be
restored by annealing. The metal is a mixture of varying propor-
tions of copper, tin, and phosphorus, the latter being added in the
form of phosphor-tin which contains about 11 per cent, of phos-
phorus. The phosphorus increases the ultimate tensile strength
and raises the limit of elasticity ; while it also acts as a cleanser
of the metal by removing any oxides formed. An average analysis
of a high grade bronze will give about 90 per cent, of copper, 9 per
cent, of tir, and 1 per cent, of phosphorus, but in some of the

B 2

52 MOTOR CAR ENGINEERING

cheaper and softer grades of metal as mucli as 10 per cent, of lead
may present. A great improvement in the homogeneity and
strength of the metal is obtained by casting by the Eatonia pro-
cess, which enables an inferior mixture to be used without sacri-
ficing either quality or ductility, while an increase in strength of
over 60 per cent, has resulted by the adoption of the process
(see Table V.). Thus, a phosphor bronze of 13'76 tons ultimate
tensile strength and 11'14 tons yield point may, when cast by the
Eatonia process, have an ultimate tensile strength of 23*09 tons,
and a yield point of 17*17 tons. The A.S.A.E. specification for
phosphor bronze is 80 parts of copper, 10 parts of tin, 10 parts
of lead, and from 005 to 0*25 part of phosphorus.

Manganese Bronze is mainly employed where non-corrosive
properties combined with great strength, hardness and toughness
are desirable, and may be cast, rolled or forged. Here the
phosphorus is replaced by either ferro-manganese or a manganese-
copper alloy, and zinc is frequently added, as is shown by the
following composition of 58 per cent, of copper, 1 per cent, of
tin, 39*5 per cent, of zinc, and 1*5 per cent, of ferro-manganese.
In a few cases a low percentage of aluminium is present, e.g.,
57 per cent, of copper, 40 per cent, of zinc, 2*5 per cent, of
feiTO-manganese, and 0*5 per cent, of aluminium; but as a rule
the copper is present in slightly increased proportions, and the
zinc is reduced below the figures given.

34. Alnminiom and its Alloys. — The alloys of aluminium
excepting aluminium bronze, which is not usually employed in
automobile work, are used principally on account of their extreme
lightness, combined with a fair measure of strength, and the
facility with which they may be cast. The usual application is
to crankcases and gearboxes, where the metal is alloyed with
varying percentages of copper or zinc — both of these substances
adding greatly to its strength and hardness without inordinately
increasing its weight — 6 per cent, of copper raising the ultimate
tensile strength from about 7 to 16 tons per square inch. This
increase in strength is, however, accompanied by a great reduc-
tion in the elongation, as is evidenced by Table V., p. 30.
Owing to the disability under which it labours in this respect
and its susceptibility to segregation, many designers are disposed
to regard these alloys with disfavour and suspicion, and to resort
to webbing and ribbing to a far greater extent than strength or

MATERIALS OP CONSTRUCTION 58

rigidity consideratioDB indicate as necessary. Aluminium alloys
should not, in general, be employed in any construction where
it is subjected to any great heat owing to its rapid reduction in
strength with rising temperature ; although cases have occurred
there it has been used for the pistons apparently without detri-
mental efifects resulting therefrom. It should also be noted
that, wherever practicable, studs should not be screwed into
aluminium, but bolts should be used. The A.S.A.E. specifica-
tions for aluminium alloys is 7 to 8 per cent, copper and the
remainder aluminium, or 2 to 8 per cent, copper, 15 per cent.
zinc, and the remainder aluminium.

A metal which has recently come into prominence on account
of remarkable properties that it possesses is duralumin, which is
manufactured by Vickers, Limited (see Table V.). This material
combines lightness with great strength, has an excellent elongation,
and may be forged, so may be used in many parts that have
hitherto been made of steel, while its resistance to corrosive
influences makes it an admirable substitute for brass, copper, etc.
It is supplied in plates, rivets, bars, wire, forgings, stampings,
channels, tees, tubes, and various rolled and extruded sections.

85. Bearing Metals. — With the object of reducing the friction
at the bearings it is the common practice to use white metal or
antifriction metal instead of phosphor bronze or gunmetal, as in
addition to possessing a low coefficient of friction, they soon
take a hard smooth skin which resists wear. These bearing
metals have only a low tenacity and therefore require some
support. This is obtained by surrounding them by shells of
gunmetal or of steel, to which they must be secured by tinning,
as otherwise there is some risk of flaking causing the subsequent
destruction of the journal.

The better class of alloys contain copper, tin and antimony, but
in some of the softer and cheaper brands of anti-friction metals
there is a very high percentage of lead, on account of the high
price of tin. Babbitt metal has a composition of 87 per cent, of
tin, 8 per cent, of copper and 6 per cent, of antimony and,
although rather expensive, gives excellent results in practice;
there are, however, many so-called Babbitt metals. Some
superior brands of white metal contain about 88 per cent, of tin,
7 per cent, of copper and 10 per cent, of antimony, whilst in the
softer of the better qualities the percentages are about 90, 8

54 MOTOR CAR ENGINEERING

and 7, respecidvely. The actual composition of the various
brands varies greatly according to the class of work upon which
they are to be employed. The effect of an increase in the pro-
portion of the copper is to harden the alloy, as does also antimony,
and raising the percentage of tin toughens it. One or two
advertised brands of bearing metals contain a little iron, lead
and bismuth, but the presence of lead is not desirable since it is
readily acted upon by tire acids in some brands of lubricating oil.

The A.S.A.E. specification for Babbitt metal is 84 per cent, of
tin, 9 per cent, of antimony and 7 per cent, of copper. Lead
may be present in the alloy to the extent of 0*25 per cent., but
the variation in the constituents from the figures quoted, should
not exceed 1 per cent, for tin and 0*5 per cent, for the antimony
and the copper.

Much may be done to increase the endurance and reduce the
frictional losses at bearings, even of the best grades of metal, by
the adoption of the Eatonia process in filling the shells ; although
some designers prefer to run the metal directly into certain parts
— the connecting rod big end, for example — as they claim that
the heat generated by friction is conducted away more rapidly
when this is done. This process has the effect of preventing the
formation of hard and soft spots in the metal due to segregation
of the different constituents of the alloy which results from the
variation in their solidifying temperatures.

In many cases^ on account of the increased strength of the
bearing metal when so cast, the shells for supporting the white
metal may be entirely dispensed with, thus effecting a saving in
the cost of machining and in the weight to be carried. An
advantage is also evident from the fact that it is unnecessary
to run the metal direct into the connecting rod end, since this
might adversely affect the results of the heat treatuient in special
steels, while renewal is rendered more expeditious and less
expensive.

CHAPTER III

GENERAL GONSIDEBATIONS IN ENGINE DESIGN

86. — When the general arrangement and design of the engine
and chassis are under consideration, among the many questions
that have to be decided are those about to be discussed.
Generally the designer and those with whom he is associated
have arrived at a more or less definite conclusion regarding these
matters as the result of past experience, the dictates of custom and
demand or perhaps the peculiar exigencies of the situation ; but
whatever the reason for the adoption of a particular construction
or line of action, it should pass under review in order that a
progressive design may be produced. It must be remembered
that finality is never reached in any class of work in every part,
although limits may be imposed in the natural order of things
which may prevent development in certain directions.

87. Cooliiig. — It is not usually difficult to decide whether air or
water cooling is to be used, as the inherent defects of air-cooled
engines preclude its employment on any but the smallest cars,
especially where prolonged runs have to be made at full power,
although cases could be cited where it has given satisfactory results
in America on engines ranging up to 40 h.-p. Air-cooled engines
must, however, be employed under a relatively light load although
it is probable that the heat efficiency is slightly higher and the
mechanical efficiency slightly lower than in water-cooled engines.
The merits and demerits of air and water cooling are discussed in
Chapter XIII., Vol. I., so it is unnecessary to recapitulate them here.

The system of water cooling — thermosyphon or forced — must
however, receive some consideration ; as both systems are fitted on
engines of equal powers in first-class work. The main advantages
attaching to the use of'a thermosyphon system are — its simplicity
and cheapness, and where a low-priced car is being produced,
these are points which have weight. On the other hand, the
reliability of a forced system of circulation, owing to its freedom
from failure due to steam or air lock, and the greater uniformity
of temperature of the cylinder, combined with the small

56 MOTOR CAR EXGDJEERIXG

risk of mechanical breakdown in modem designs, makes its
employment eminently desirable. Each case must, therefore,
be determined when all the conditions as to power, price, the
class of vehicle, and circumstances under which it is to be em-
ployed are known. It may be remarked however that, for colonial
service, a forced system becomes imperative, owing to the
possibility of a restricted water supply in scattered districts.

88. Luiricatioii. — The same general observations made in the
preceding article respecting the factors that influence the designer
in deciding what cooling system shall be used apply with equal
force to the lubrication of the engine — whether it shall be splash
or pump fed — the latter including both the trough and the forced
systems together with the various modifications that are found in
current practice. The use of the simple splash system of lubrica-
tion is accompanied by such drawbacks that only the greater
expense incurred by the other systems can justify its existence on
any engine and it is therefore very seldom fitted to any but very
low-priced cars and some motor-boat engines. As regards the
other two forms, the Author can well recommend the fully forced
system to more general employment, because splash in any form
is, in his opinion, inferior, seeing that a large quantity of oil must
always be in the system to render it effective and even then the
oil which reaches a bearing may have become vitiated by a contact
with the piston and the cylinder walls or by exposure in the
orankcase. In a fully forced system, one can be assured that
clean oil is being directed in sufficient quantity to the exact
place where oil is necessary, at all speeds and under all conditions
of service, thus effecting a great saving in the cost of upkeep as
well as that of the lubricant itself, while its cooling effect during
prolonged runs cannot be disregarded. The engine will also have
a purer exhaust. Naturally, such a system is more expensive to
supply in the first instance because of the greater care and skill
required in fitting and adjustment ; but not greatly so, especially
where the troughs are mechanically controlled so as to enable
the depth of immersion of the dippers to be varied ; and
hence any disadvantage under which it may labour in this
direction will be more than compensated for by the benefits
which may accrue from its adoption.

The ultimate selling price of the car is, however, not without
some influence in this, as in other directions, for many refinements

GENERAL OONSIDEKATIONS IN ENGINE DESIGN 57

58 MOTOR CAB ENGINEERING

that would be desirable mast be excluded on account of the addi-
tional cost involved and for ordinary purposes the conditions are
such as to render it questionable whether the increase in the initial
outlay which a fully forced system may entail would be appre-
ciated at its true value, in view of the fact that less elaborate
sydtems have proved so satisfactory in service as regards power
developed, oil consumption, silence, etc. Still, in the case of
engines having small cylinder dimensions such as are so largely
used at the present day, which, in order to obtain sufficient power
must necessarily be run at comparatively high speeds of revolu-
tion, it would appear that the use of forced lubrication is highly
desirable, since for the greater portion of their service they are
required to develop a high proportion of their power ; while, in
larger and more powerful engines, which are seldom called upon
to give their maximum output, it is not so essential.

Completely forced systems of lubrication are, however, gener-
ally used on engines in which the workmanship is of the highest
quality and where expense is a secondary consideration, not that
all other engines are necessarily inferior, or that engines so
fitted are, ipso facto, all that is to be desired ; but generally, the
best makers embody in their designs some fairly extended
system of forced lubrication, for example, splash lubrication to
the gudgeon pin, and forced lubrication to the crankshaft bear-
ings ; or trough lubrication is provided for the crank and
gudgeon pins and forced lubrication is used at the main bearings,
while others use trough alone, the main bearings being provided
with oil wells to catch the oil. For such designs as sleeve
valve engines, trough lubrication is perhaps always the prefer-
able arrangement. The matter is, however, discussed more fully
in Chapter XII. and in Vol. I., pp. 811 — 314).

89. Number of Cylinders and the Method of Casting. — In a large
measure the horse-power required to be developed and the public
demand will govern the number of cylinders employed in the
design, but in considering the relative merits of multi-cylinder
engines, it is well to know what qualities contribute to the pro-
duction of a satisfactory and a commercially successful engine.
They are — efficiency, silence, low running costs, durability,
reliability, flexibility, lightness and accessibility.

It will be manifest that any reduction in the number of moving
parts in an engine must conduce to a higher mechanical efficiency

GENERAL CONSIDERATIONS IN ENGINE DESIGN 59

while, neglecting the speed of revolatioo, the larger bore of
cyHnder for any stated horse-power will raise the thermal efficiency
on account of the lower heat loss to cooling water, and, therefore,
favour a reduction in the number of cylinders. But this will be
largely discounted by the less effective carburation which results
from the less uniform flow of air through the carburetter. As
regards silence — for any given power, tlie greater the number of
cylinders, the less the maximum load from the explosion of the

Fio. 5.— 30 h.-p. 1913 Sheffield Simplex Engine— Cross -section.

gas in the cylinders, and therefore the impulses will be less
violent. This must only be interpreted in a general sense as
the real cause of the greater silence is the reduction of vibra-
tion, resulting from the decrease in the torque variation and the
superiority oE the four-cylinder over the two-cylinder engine and
of the six-cylinder over the four-cylinder engine in respect of
balance ; but at the present time many engines have been made
mechanically quiet by the careful construcLion and design of the
valve gear and the lightening of the reciprocating; parts without
any great sacrifice of efficiency. But as the number of impulses
per revolution increases, there is a more even torque and less

60 MOTOR CAR ENGINEERING

shock on the tranBmiseion gear, less wear upon gearing and upon
tyres, and as the carburatioo is more perfect, the cost of main-
tenance is reduced on two of the principal items of car expendi-
ture — tyres and petrol. The flywheel fitted to practically any
engine will, at moderate and bi<;h speeds, transfer the twisting
moment on the crankshaft into a uniform torque on the trans-
' mission ; but at lower revolutions, say, below about 800 per
minute, there may be a considerable variation in torque with a

Fig. 6. — 30 h.-p. 1913 Sheffield Simplex Engioe — End view.

small number of cylinders. It is probably largely from these
causes, combined with the greater value attributed to tliat
nebulous quality — smooth running — and the relative smaller im-
portance of expense, that makers appear to prefer an increase in
the number of cylinders to using a bore much in excess of
100 mm. Some saving might also be anticipated in the cost
of repairs, but because of the greater number of parts subject to
wear and which will require adjustment or renewal, the multi-
cylinder is, probably, at a disadvantage in this respect.

Regarding durability and reliability, these are but slightly
affected by the number of cylinders, all the better-class cars

GENERAL CONSIDERATIONS IN ENGINE DESIGN 61

being practically immune from trouble under these heads. It
may, however, be pointed out that the weight of the reciprocat-
ing parts tends to increase at a more rapid rate than does the
cylinder bore, and hence the loads due to inertia effects, which
are detrimental on the non-power strokes, are higher; but
within the limits of dimensions ordinarily employed in automobile
engines, and since the bearing areas will be correspondingly
increased with the larger piston area, it is not considered that
any appreciable factor is introduced on this account.

The accessibility of multi-cylinder engines is, perhaps, superior
to that of those having a lesser number of cylinders, because any
dismantlement may be more readily effected on account of the
size of the parts to be handled, and means for access to the crank-
case interior can be more easily provided, if desired. On the
other hand, there are more parts liable to derangement or which
are likely to require attention, and in some engines the cylinders
are cast en bloc ; but it is not possible to generalise on account
of the wide effects of variations in the arrangement and details of
design adopted. As regards flexibility, the multi-cylinder engine is
undoubtedly the superior, as although the flywheel has a greater
capacity the less the number of cylinders, its effects at low speeds
of revolution (where it is mostly of value) are not comparable to
the greater uniformity of torque and better carburation results
from the more continuous flow of air through the carburettor.

On the question of the relative weights of engines, it is very
difficult to obtain definite data upon which any effective
comparison can be made, on account of the great variation in the
construction adopted and in the grades of materials and stresses
employed ; but there is little doubt that the weights of the flywheel,
the transmission gear, etc., may be considerably lessened as the
number of cylinders increases on account of the small variation
in torque. It should be observed, however, that for any stated
power, the larger the number of cylinders employed, the greater
will be the length of the space taken up by the engine, and this
will tend to curtail the space available for seating accommodation.

From the preceding the general superiority of the multi-
cylinder engine will be apparent, but there still remains one
other aspect of the question to be considered ; namely, that of
first cost. It is obvious that any increase in the number of parts
to be handled and subjected to the various operations during

62 MOTOR CAR ENfilNEERING

manufacture must raise the cost of production, and therefore
necessitate a higher seUing price. Much therefore depends upon
the question as to whether or not a sufGcieatly extensive market
cun. be found and each case must be determined on
its merits. Of late years there hoe been a demand for a four-
cylinder low-powered car, and this has been met by a large

Fio. 7.— 50 h.-p. 1914 Sheffield Simplex Engine- Crosa-section.

number of manufacturers, but it would he unreasonable to
expect Buch a car to be produced at the same price, as, say a two-
cylinder car of equal power.

With the object of improving the appearance of the engine by
the elimination of a large amount of external piping and reducing
the cost of manufacture by facilitiLting machining and assembling
operations, many firms have in recent years adopted the en bloc

GENERAL CONSIDERATIONS IN ENGINE DESIGN 68

system of cylinder casting. The system is not without merit,
for in addition to the above, there are fewer joints to be made
or broken, the carburation is improved because the incoming
gas is in contact with heated surfaces for a longer time, the heat
thus utilised in vaporising the fuel assists in cooling down the
cylinders, the length and weight of the engine can \te reduced,
and the cylinders assist in resisting the distortion of the crank
chamber. The latter is, however, a questionable advantage
since it should be unnecessary for the crankcase to rely upon
any other part for sufficient rigidity. But with such castings
there must always be some difficulty in ensuring clear passages
for the inlet and exhaust gases and for the cooling water, and
in obtaining a uniform thickness of metal of a homogeneous
nature in the walls of the cylinders — especially when the induction
or the exhaust pipes are cast integral with the main castings— on
account of their intricacy. Variation in the thickness of metal
is objectionable because of the distortion produced by unequal
expansion when the casting is heated up under working con-
ditions, and is markedly so if there is a strip of metal uncooled
between two adjacent cylinders. These difficulties have been much
reduced in modern foundry work and by efficient design, so that
some firms produce castings which are guaranteed to be within
one-sixteenth of an inch in the bore, as cast, but it is only necessary
to examine a section through some finished castings, in order
to see that the defect has not been entirely eliminated.

The dismantlement of an engine with cylinders cast en bloc
and the subsequent reassembling is also not an easy matter,
although the size of the casting affects the question considerably ;
still the operation of entering four pistons into their respective
working cylinders of a mono-bloc casting cannot be considered to
be within the capabilities of many owners, and a defect in any
one cylinder due perhaps to softness of the metal, porosity or
damage, necessitates the renewal of the whole casting. It will,
generally be found to be a somewhat difficult matter with
mono-bloc cylinders to obtain a bearing between each crank,
unless the centre lines of the cylinders are spread rather more
than is usual (compare Figs. 8 and 11), although there is no real
Necessity for this in ordinary touring engines provided that the
crankshaft is correspondingly stiffened up, and this is especially
the case when there is no water space between the cylinders ; while

64 MOTOR CAR ENGINEERING

if the valves are all arranged on one side, the provision of ample
valve area, without the use of excessive lifts is rendered very
far from simple, particularly in high-speed engines having a
high stroke-bore ratio. There is also a greater possibihty of
some variation in the volume of the compression spaces with
mono-bloc cylinders, which is likely to adversely aflfect the smooth
running qualities of the engine. Both the single and the pair
cylinder construction have the advantage that it is possible to
utilise either two, four or six separate cylinders, or one, two or
three pairs of cylinders with their pistons, valves, etc., for three
different models in obtaining a range of powers.

On the whole it would seem to be desirable to compromise and
arrange the cylinders in groups of two or three, at all events for
engines with bores in excess of 80 mm. as, is now customary,
as then the extreme effects indicated are not obtained, while
a more rigid cleaner and cheaper engine is produced.

40. Piston Speed, Bevolutioiis and Stroke. — There are five
principal factors that impose a hmit upon the piston speed of an
engine : —

(a) The weight of the pistons, connecting rods and the recipro-
cating parts of the valve gear.

(b) The areas through valves and passages.

(d) The effectiveness of the engine lubrication.

(e) The ignition of the charge.

Of these, the first is the most important and it is not too
much to say that the modem high-speed engine would never
have been produced except for the attention which has been
paid by designers to the problem here represented. Lightness,
combined with strength and stability, is one of the secrets of
success in automobile engine design, because the magnitude of
the inertia forces introduced by the employment of high speed
increases rapidly with an increase in speed, as does also the
vibration produced by the unbalanced forces and couples which
it is not possible to entirely eliminate in two, four and even in
six-cylinder engines; and at very high engine speeds, the
reversals of pressure at the bearings which take place when the
load due to the force required to overcome the inertia of the
reciprocating parts rises above or falls below the load due to the
pressure in the cylinder which is acting upon the piston.

GENERAL CONSIDERATIONS IN ENGINE DESIGN 65

together with the heavy inertia loads apon the bearings, may
introduce effects that are decidedly objectionable. As regards
the latter, it may be pointed out that although at moderate
speeds the influence of inertia is in the direction of relieving
the bearing pressures from the full explosion effects, a limit —
depending upon the weight per unit of piston area — is ultimately
reached beyond which increase in speed rapidly raises the load
to which the bearings are subjected on the non-power strokes.
This limit is, however, above the speeds at which engines are
normally run, and hence is negligible except in special instances
— in racing engines, for example, and in such engines the
piston, etc., is generally lightened to a degree that would hardly
be permitted in ordinary work. Mention must also be made
of the reciprocating parts of the valve gear, which, since the
valves are opened by a cam and closed by a spring, must
be made as light as possible if high speeds are to be attained,
in order that the operations may be rapidly effected without
causing high stresses in the actuating mechanism and necessi-
tating the employment of unduly strong springs.

In the present day engine, by the use of higher grades of
material, and by careful attention to the detail construction, the
weight of the reciprocating parts has been much reduced, until
a point has now been reached in some designs beyond which it is
difficult to see what further progress can be made without
impairing the stability, except with regard to the valve gear, and
even here it is not anticipated that much can be done in this
direction with the poppet type of valve.

Maximum piston speed is also largely a matter of valve area,
as if the valve areas are sufficiently large to permit of the induc-
tion and expulsion of the gases with sufficient rapidity and with-
out throttling, the speed can be raised indefinitely without any
decrease in the engine torque. But it is well known that, in any
engine, after a certain speed of revolution is reached, the curve
of torque commences to fall off rapidly owing to the restricted
passages through the valves and the high gas velocities which
are then attained, notwithstanding the fact that the lower
heat loss to the cooling water which takes place at the higher
speeds from the shorter time during which the gases are in con-
tact with the cylinder walls tends to raise the mean effective
pressure upon the piston, although the latter is probably partly,

M.C.E. F

66 MOTOR CAK ENGINEERING

and perhaps wholly, neutralised by an increase in the amount of
internal friction at the pistons, bearings, &c. Large valve areas
necessitate the use of either larger diameter valves or high lifts,
and these, in conjunction with the high speed at which the valves
are operated, cause high inertia stresses in the actuating gear,
noise and vibration ; while with the larger diameters there is some
difficulty in securing an entire absence of valve leakage. If the
valves are arranged all on one side, the diameter of the valve is
limited by the space available in the length of the engine,
although some increase becomes possible if the valve centres are
staggered; at the same time, it should be observed that large
valves neceiisarily entail the use of ample valve pockets, which
tend to limit the compression ratio it is convenient to employ,
and increase the cooling surface. In such circuxQstances it is an
advantage to slightly incline the valves with respect to the centre
line of the cylinder as shown in Fig. 12. It may be added that
the preceding remarks concerning the importance of large valve
areas apply in some measure to carburetters; although not
perhaps to the fullest extent, because by suitably shaping the
passages the resistance to air flow may be only increased by a
small amount.

41. The influence of the stroke-bore ratio also merits some
attention, as experiments have shown that as this increases, so
does also the limit of piston speed, doubtless partly due to the
speed at which the valves are actuated and the greater volumetric
efficiency for the same valve area, but the allowance that should
be made to account for their effect on piston speed is not by any
mea'ns agreed upon. This is probably attributable to the marked
influence of other factors, such as the skill employed in the
design and construction of the engine, the weight of the recipro-
cating parts, &C., all of which tend to obscure the real effects
produced by varying the ratio, if the results of tests made on a
large number of different types of engines are examined.

The I.A.E. Committee^ on the horse-power rating of petrol
engines investigated this question and proposed the formula —
Piston speed = 600 (r + 1) feet per minute = 8 (r -}- 1) metres
per second, where r is the stroke-bore ratio, as expressing the
speed that may be reasonably expected to be attained in well-
designed and carefully constructed engines; but it was never

1 Proceedings I.A.E., Vol. V., " The Rating of Petrol Engines "

GENERAL CONSIDERATIONS IN ENGINE DESIGN 67

intended that this should represent the absolute limit, in fact,
several engines in cars engaged in the Standard Gar Race of 1911
ran at speeds in excess of those calculated in this manner.

The speed of ignition of the charge is of no importance so far
as design is concerned, where engines for touring cars are under
consideration, as magneto construction has progressed so rapidly
that the spark produced at the plug is always ample to effectively
ignite the gases. But in the case of engines running at
extremely high speeds and where the maximum of power is
required — as in racing engines — the speed of the flare through
the gas may be insufficiently rapid if only one plug is fitted ; and
in such engines double ignition may with advantage be employed.
It may be added that the higher compression which is generally
used in racing engines, of itself, conduces to a more rapid ignition.

The lubrication is also a factor that seriously affects the upper
limit of the piston speed, as well as the revolutions, since unless
the supply of oil is sufficient at all times to maintain the oil film
between the supporting surfaces, abrasion must inevitably take
place ; while the beneficial results to be derived from the pro-
vision of an ample quantity of lubricant, through its cooling effect
on the bearings, cannot be over-estimated.

With regard to the question of stroke and revolutions, con-
siderable diversity of opinion exists as to the relative merits of
long and short stroke engines, because although the latter class
can run at higher revolutions without setting up excessive
vibration or causing distortion — on account of the great im-
provement in the materials, construction, etc. — the long stroke
engine can be made to be almost as free from trouble in this
respect, and from the higher piston speed it is possible to attain
there should be a greater amount of power developed per unit of
cylinder volume. Furthermore, the cooling surface volume ratio
is greater in a short stroke engine than in one with a long stroke,
the difference being most marked when the engine is on the
inner dead centre ; and hence, as the heat loss to the cooling
water is less with the latter, a higher mean effective pressure
should be obtainable. It may, however, be remarked that by
increasing the compression ratio (not necessarily the compression
pressure) the loss of power from this cause may be neutralised
without producing any tendency to hard running or increase in
noise.

F 2

68 MOTOR CAR ENGINEERING

The increased vibration may be attributed to the increase in
the magnitude of the unbalanced forces, owing to the reduction
in the ratio of length of the connecting rod to the crank radius,
which practically always accompanies an increased stroke, also
to the greater variation in torque with long stroke engines ; to
the slightly heavier reciprocating masses; and partly to the
longer connecting rods and crank webs employed and the less
compact design. Experiments have shown that the transverse
inertia loading of the connecting rods causes them lo be deflected
to a marked extent, while the vibration resulting from the deflec-
tion of the crankshaft under centrifugal force has also been
clearly demonstrated. It should be observed that the inertia
forces in the line of stroke vary directly as the stroke, and as the
square of the angular velocity of the crankshaft ; so that for the
same piston speed they will be less in the long stroke engine
than in the short stroke engine. But there is probably very
little, if any, advantage to be gained from this, by the adoption
of the longer stroke for ordinary touring car engines, as, apart
from the fact that the reciprocating parts are thereby increased in
weight, it is usual to run the engines at approximately the same
speed of revolution in both types of motor. On the other hand,
the short stroke engine is probably more flexible or controllable,
if flexibility is interpreted as meaning the production of a good
torque at low and high engine speeds and not simply an ability
to run at a low speed of revolution or a low piston speed, which
is largely dependent upon the fly-wheel capacity. It is not so
heavy because a smaller crankcase and flywheel are possible,
and it has less height, while the transmission gear is lighter
because of the higher revolutions. It is also probable that larger
diameter valves may be employed, and hence a higher volumetric
efficiency will be obtained with a consequent increase in power.
In the case of the small bore, high speed engines which have
now come into such extensive use, and in commercial vehicles,
where the car speeds are low, the high reduction gear in the rear
axle which becomes necessary with abnormally short strokes pre-
sents a very difficult problem for solution; and it is probable
that this accounts for the high stroke-bore ratios employed in
small power cars.

These aspects show that it is difficult to arrive at any definite
conclusion on the matter, although it would appear to be desirable

GENERAL CONSIDERATIONS IN ENGINE DESIGN 69

to avoid the use of excessive ratios, and further investigation only
serves to render it more complicated, as there are so many in-
fluences that are variable in their effect upon each individual
factor mentioned. The most suitable ratio of stroke to bore for
any particular class of work must, therefore, be subject to the
variations which must inevitably result from the dictates of
experience.

At the present time the stroke-bore ratio varies from 1 up to 2,
but the majority of manufacturers keep within the limits of about
1*3 and 1'8, the lower values being more common with all sizes
of engine, but especially on the larger engines ; and where higher
ratios are employed it is usually for the purpose of taking the
fullest advantage of horse-power rating rules.

It is generally, however, undesirable to exceed a piston speed
of approximately 1,200 feet per minute (6 metres per second)
under normal running conditions, as this is, roughly, the speed
of maximum torque in engines used for ordinary touring cars,
and higher speeds usually entail some sacrifice in the smooth,
quiet running and wearing qualities of the engine; and the
gearing, etc., should be proportioned on this basis. Higher
speeds are attainable, and those quoted will be influenced by the
factors mentioned in Art. 40, but at from 1,600 to 1,800 feet per
minute (8 to 9 metres per second) the maximum power is usually
developed ; although in special engines, for example, those having
very light reciprocating parts, large valve areas and direct inlet
and exhaust passages, the torque curve may be maintained until
a speed of from 1,800 to 2,000 feet per minute (9 to 10 metres
per second) is reached, and the speed of maximum power may be
between 2,500 and 2,800 feet per minute (12*5 to 14 metres per
second), or even higher.

42. There is another aspect of this question to which attention
may be drawn, namely, what is the highest speed at which an
engine can be run for an indefinite time under its maximum
load? Tlie most potent factor affecting this is, probably, the
effectiveness of the lubrication, which, in turn, is largely depen-
dent upon the pressures to which the crankshaft bearings are
subjected and the viscosity of the lubricant. The load upon the
bearings is determined by the pressure upon the piston and the
inertia of the reciprocating parts, while the viscosity of the oil
varies with its temperature, and this, in any given engine, will

70 MOTOR CAR ENGINEERING

greatly depend upon the bearing pressures. Hence, if the maxi-
mum bearing load is reduced, it is reasonable to suppose that the
engine will run for more prolonged periods before trouble is likely
to occur, despite the fact that it is reached more frequently.
The maximum bearing pressures are due either to the inertia
forces acting in the line of stroke, or to the pressure on the piston
at ignition less these inertia forces; but at high speeds the
former is the greater, and therefore, by equating the force required
to accelerate the reciprocating and rotating parts at the com-
.mencement of the induction stroke to the difference between the
load on the piston and the inertia forces acting at the commence-
ment of the power stroke, the engine speed under full load for the
most prolonged effort will be obtained. Thus : —

Ma)V (l + i) -f MicoV = P^ - Ma)V (l + 1) - Mia>V

where M is the mass of the reciprocating parts. Mi is the mass
of the connecting rod considered as rotating with the crank, to is
the angular velocity of the crank in radians per second, r is the
radius of the crank in feet, n is the ratio of the connecting rod to
crank radius, P is the ignition pressure in lbs. per square inch,
and d is the diameter of the cylinder in inches —

'. • . 2Ma>«/' (l + ~) -f 2Miu>V = P^'

and

Pird^

(02 =

8rlM(l-fi)-fM;}

Since N = the number of revolutions per miqute =

277

JJ2 _ 900a>«

TT*

P7rd« ^ 900

7r2

= 35-8 , ^^\^ = 1,158 ^^^

r{M(l + i) + M,( rlw(n-^)+W,}

where W is the weight in lbs. of the reciprocating parts, and Wi
is the weight in lbs. of the portion of the connecting rod con-
sidered as rotating with the crank —

GENERAL CONSIDERATIONS IN ENGINE DESIGN 71

N = 34d J.

,jw(n-l) + w.}'

But S = mean piston speed in feet per minute ^ 4rN —

S = 186d ' ^'

w(l + i) + Wi

At the speeds given by the above equations the bearing pres-
sures on the same dead centre of the crank will be equal irre-
spective of the cylinder operations, and the ratio of the load on
the in-centre to that on the out-centre will be as (n + 1) is to
(n — 1). It is worthy of notice that the piston speed varies as
the square root of the stroke, which is slightly less, for the pro-
portions usually employed, than that which was suggested by the
I.A.E. Committee above referred to.

43. Compression Pressure. — It was shown in Art. 97, Vol. I.,
that the thermal efficiency of the petrol engine depends upon its
compression ratio, and therefore for a higher efficiency the com-
pression pressure used in an engine should be as high as possible.
But there are other considerations which influence the designer,
namely, the risk of pre-ignition and, in the case of cars used
for pleasure or commercial purposes, the importance of comfort
and silence in operation. The former arises from the fact that
as the pressure increases during the compression stroke, so does
also the temperature of the mixture, and therefore by raising the
compression sufficiently it is possible to cause a spontaneous
ignition of the charge. The actual pressure at which this takes
place is difficult of determination, seeing that phenomenal com-
pressions have been employed on some racing engines without
undue trouble from this cause. It is probable that at the high
speeds of revolution employed in these engines when under full
load, the time of pre-ignition synchronises approximately with the
correct time of spark ignition for such speeds ; but it is inadvisable
from this cause alone to exceed, say, 100 lbs. per sq. in. (0'07 kilos.
per sq. mm.) or a compression ratio of 4*9 for ordinary work on
^ater-cooled engines if liability to this defect is to be avoided,
for extremely thin layers of carbon deposit will, in high compres-
sion engines, cause pre-ignition. In air-cooled engines the com-
pression ratio should, preferably, not exceed 4*0.

72 MOTOR CAR ENGINEERING

It should, however, be observed that increase in the compression
ratio, while limited by pre-ignition, generally involves an increase
in the ratio of cooling surface to cylinder content, and, therefore,
an increase in the cooling losses, so that it is possible with certain
compression ratios for the loss of heat due to the proportionately
greater cylinder surface in contact with the jacket water to reduce
the pressure sufficiently to neutralise the effects of raising the
compression ratio. This was shown to be so in the course of
experiments carried out by Professor Watson,^ as the relative
efficiency diminished rapidly as the compression was increased,
and there was little or no gain in the thermal efficiency. Professor
Gallendar also remarks^ that the stroke-bore ratio must be
increased in order to obtain any appreciable advantage from
increasing the compression ratio. At one timB it was usual for
small bore engines to have a higher compression ratio than those
of larger bore, owing to their greater heat loss ; but at the present
day there is little, if any, difference in the values employed.

As regards the effect of compression upon the quiet running of
an engine, it is clear that as the pressure at ignition increases
with the compression pressure, the explosion effects will become
more pronounced and the vibration will be greater in an engine
using a high compression than in another with a low compres-
sion, due to the greater variation in the torque of reaction which
depresses the frame on the springs on the off side, and tends to
lift the frame on the near side of the car ; while leakage of gas
will be more in evidence. Further, there will be a greater diffi-
culty in starting up, especially in large engines, increased wear
and tear upon the engine parts and transmission, a greater varia-
tion in crank effort, a less comfortable car, and a tendency to
hard running. For these reasons one occasionally finds that,
notwithstanding the sacrifice in efficiency which is entailed,
nominal compression pressures as low as 55 lbs. per sq. in.
(0*04 kilos, per sq. mm.) or a compression ratio of 3'3 are
employed, although usually from 70 to 85 lbs. per sq. in. (from
0'049 to 006 kilos, per sq. mm.) or a compression ratio of from
3-78 to 4-42 is used. (See also Art. 62.)

44. Type of Ignition. — Generally there will be little difficulty in
deciding this factor in the design. On account of the inherent

* Proceedings I.A.E,^ Vol. III. pp. 467, &c.
3 Proceedings I.A.JS.y Vol. V. p. 262,

GENERAL CONSIDERATIONS IN ENGINE DESIGN 73

defects in low tension ignition for high speed engines and the
consequent almost universal adoption of the high tension system,
it is only necessary to consider whether high tension magneto,
coil and accumulator, dual, duplex or double ignition, or the
combined ignition and lighting system is to be adopted.

In general, having in view the high efficiency of the modern
magneto, it may be accepted that the dual ignition will only be
fitted on the more expensive and high-powered cars and duplex
ignition on the better class of lower-powered cars to facilitate
starting up, as the fitting of such can only be regarded as
refinements, although very desirable with engines of large bore,
and therefore only to be provided where other considerations
besides that of actual price receive attention. These remarks
apply where the system of ignition is to be fitted as standard
practice, but in many cases either dual or duplex ignition is
optional and is quoted for at an extra price. Mention should
also be made of Bosch hand-revolved magneto, which is fitted on
the dash-board and enables a series of sparks to be obtained
when the engine is not working without the use of a coil and
battery, thereby providing a most effective form of switch starting
if there is an explosive mixture within the cylinder, but which
may be coupled to the starting handle so that it is unnecessary
to crank the engine very quickly in order to obtain a sufficiently
strong spark to ignite the charge when starting from cold. This
system must be regarded as an optional fitting.

In a similar manner, one may expect to find coil and accumu-
lator ignition only on cheap, low-powered cars, where every
endeavour is made to reduce the selling price; but seeing
what little difference there is between the price of this system
and that of ordinary magneto ignition and in view of the advan-
tages accruing from the use of the latter, it would seem desirable
to employ the magneto in all cases where only one system of
ignition is fitted. This is now generally appreciated, with the
result that the magneto is almost always, if not universally, fitted
on all modern cars ; sometimes, however, it is supplemented by
a separate coil and accumulator system.

As regards double ignition, a form of two-point ignition where
a magneto with two distributors is employed, this is mainly,
although not exclusively, used on racing cars, but will be fitted
when specially ordered. Two separate coil and accumulator and

74 MOTOK CAR ENGINEERING

magneto systems of ignition are seldom applied to modern cars,
and these are of the most luxurious type; but some form of
synchronised ignition was at one time extensively adopted.
Regarding the combined ignition and lighting system, it is not
at all improbable that, with the more extensive use of electrically
operated self-starters, this system will eventually be largely
employed, although the increased cost involved and the excellence
of the modern magneto will tend to retard its adoption. But
where an electric lighting syatem is to be installed on the larger
cars its simplicity and low cost of upkeep render it worthy of the
attention of designers.

46. Type of Engine. — There is probably no other branch of
engineering in which it is more necessary for the manu-
facturer to have his finger upon the pulse of the buying public
than in automobile work. Much can be and is done in educating
the prospective purchaser to an appreciation of the merits of some
particular design, but the ultimate test of success is a commercial
one — the sale of cars embodying such construction. It is there-
fore obvious, that even though the design may have many inherent
advantages, it will be impossible for a manufacturer to continue its
employment unless the sales are sufficient to warrant its retention.

This is well illustrated by the two-stroke engine and the four-
cylinder horizontal engine with opposed cylinders, both of which
are superior in some respects to the ordinary vertical engine — the
former as to simplicity, weight and space, and the latter with
regard to balance and vibration — yet little has been done to
improve either of them, largely on account of the conservatism
of the motoring public. It must be admitted, however, that
two-stroke engines as at present constructed labour under many
disadvantages, except in one or two special cases, and in these
the additional mechanism introduced to overcome inherent
defects tends to diminish the advantages mentioned above. But,
in general, the leakage of fresh gas to exhaust during cylinder
induction, or from the crank-case, as well as the lack of homo-
geneity in the mixture, reduces the thermal efficiency by about
25 per cent. ; the throttling down required when low powers or
speeds are developed causes imperfect scavenging and renders
the engine less flexible ; while the period during which the ports
are uncovered is insufficient at high-engine speeds to admit of
the full charge of gas being taken, or of the complete expulsion

GENERAL CONSIDERATIONS IN ENGINE DESIGN 75

of the exhaast being effected, and thus the torque curve falls off
more rapidly. These . deficiencies are, however, now being
remedied, and the two-stroke engine may eventually become a
serious competitor with the conventional four-cylinder engine.

The horizontal opposed engine also suffers somewhat by com-
parison with the more conventional type on account of the cleaner
and neater arrangement of the latter and the excessive width
of frame, the less effective access and the possibility of lubrica-
tion troubles arising with the former. It is sometimes stated
that the cylinders have a tendency to become oval with horizontal
engines, due to the wear down of the piston ; but this is not so, as
the weight of the reciprocating parts is but a small fraction of
the side thrust on the cylinder walls.

When^ therefore, an engine has to be designed, it will be the
four-stroke vertical type that will receive consideration, as the
few exceptions to this rule will be those in which some patented
feature is embodied, and these require special treatment.

46. Engine Arrangement. — From the foregoing the principal
characteristics of the proposed design will have been practically
determined, and the general arrangement and construction of the
details may now be considered. In examining the various
possible alternatives special attention should be directed to the
necessity of affording adequate means of access to all parts that
are likely to require frequent adjustment, examination or renewal,
and for the ready dismantlement of any part with the least
possible derangement, especially in cars which are likely to be
in the hands of an owner-driver ; at the same time, however, the
importance of the cost of manufacture, the appearance of the
engine, and cleanliness should not be overlooked. The general
disposition and the method of driving the camshafts, oil, water
and air-pumps, magneto, distributors, commutator, dynamo, fan,
the details of a self-starting system (pump, distributor, motor,
dynamotor, &c.), if such is to be fitted and even when it is made
optional, the system of engine suspension, the form of crank-
shaft and type of valve gear, the arrangement of the inlet and
exhaust piping and the control system, as well as the location
of the oil and petrol filters and fillers, oil level indicator, and
every other fitting the position of which may be varied, should
pass under careful review as integral parts of a complete
machine. This critical examination should not be dispensed

76 MOTOR CAR ENGINEERING

■

with even when the engine is to follow «Iong the lines of a
previous model, as apart from the fact that design is a pro-
gressive science, the introduction of some new feature may
detrimentally affect the accessibility and appearance of the engine,
but which might be entirely obviated by a slight re-arrangement
of the component parts. This is one of the reasons why a
construction which has proved quite satisfactory elsewhere'
should not be incorporated unaltered without adequate considera-
tion as to its probable effect upon the existing arrangement.

It is usual to arrange the carburettor and the magneto on oppo-
site sides of the engine in order to minimise the risk of an explosive
mixture of air and petrol vapour being in the vicinity of the
magneto, and which, if a short circuit should occur, might
become ignited ; but although desirable, it is questionable whether
it is imperative with modern accessories so long as they are not
too close together. The arrangement, however, necessarily
follows from the conventional methods of driving the magneto
(see Figs. 11 and 18), namely, either by a cross-shaft in front
of the engine, or by a longitudinal shaft, usually on the valve
side of the engine, while the carburettor is so placed because of
the better carburation obtained when the incoming charge passes
through a passage formed within the water-jacket ; but the
factors influencing this, as well as the other matters above
mentioned, are discussed in the succeeding chapters relating to
them. (See also Vol. I.)

From the foregoing the size and shape of the crankcase is
closely determined, as well as the space required for the engine
and its component parts, not only when in position, but also
when assembling or dismantling the individual parts or the
engine unit complete, while the centres of the shafting will also
be approximately determined. The transverse section of the
crankcase is very closely fixed by the clearance necessary for
the crankshaft, connecting rods, camshafts and the lubricating
arrangements ia the base of the crank-chamber ; and the overall
length by the bore and construction of the cylinders, the pro-
posed water thicknesses, the lengths of the crankshafts, bearings
and thickness of the crank-webs, and the width of the case
enclosing the timing wheels.

CHAPTER IV

POWER REQUIREMENTS

47. Katnre of the Sesistances to be overcome. — In Vol. I. p. 116,
it was stated that the power available at the roadwheels is
employed in overcoming the following resistances : —

1. Boiling resistance.

2. Besistance due to gradient, which may be either positive or negative.

3. Resistance due to the air, which may also be either positive or negative.

These are, however, the resistances encountered by a vehicle
when travelling at a uniform velocity ; but when the speed of a
car is increased the torque transmitted by the engine must be
augmented by an amount sufficient to produce this acceleration
as well as to overcome the increase in the resistance to traction
at the higher speed. Hence power will also be utilised in this
direction.

In ascertaining the power required to perform certain work
in ordinary engineering practice, the conditions of service can
usually be definitely settled, but the designer of the petrol engine
for a car is confronted by two principal difficulties, the first being,
that the factors above mentioned cannot be stated in exact terms,
either from the lack of reliable data upon which to base an
estimate, or from the great variation in magnitude to which each
is subject, so that any values which are assumed in the design
may be liable to a considerable degree of error. The second is,
that the weight and shape of the body to be subsequently
fitted, the load to be carried, the maximum gradient which the car
must be able to climb, the areas subject to air pressure, and the
resistance offered by them to propulsion are often not accurately
known.

There are also two other factors which have an important bear-
ing upon .this question, namely, the necessity of producing chassis
of more or less standard dimensions and design, in order that the
selling price may be kept within reasonable limits and permit a
fair profit to be made ; and the demand of the buying public for

78 MOTOE CAR ENGINEERING

an engine of a definite rated horse-power, or of certain cylinder
dimensions — the latter being frequently the dominating factor,
and where such is the case, the designer must proportion the
gearing so that the maximum power which the engine is capable
of developing is sufficient to overcome the resistances to motion.

The power to be developed by an engine, therefore, either
determines the speed of the car, if the resistances are fixed ; or
is determined by the tractive effort which must be applied at the
road- wheels in order to overcome the normal resistances to motion,
and by the speed of the car ; but not exclusively so, as in high-
powered cars and even in some cars of quite moderate power, the
maximum engine torque at any given speed is in excess of that
generally required for propulsive purposes alone (excepting at
high car speeds on heavy roads, or on exceptionally stiff
gradients) in order to give greater ease and comfort in driving,
to allow of the more extensive use of the quieter direct drive and
to permit a higher average speed to be attained than would other-
wise be possible.

The relation between the power available at the road-wheels,
the speed and the tractive effort may be expressed by —

HP _ FS ^FV
""33000 375

where F is the tractive effort in lbs., S is the distance moved in

feet per minute, and Y is the speed of the car in miles per

hour.

The value of F is the summation of the resistances indicated at

the commencement of this article, while S and V will be mutually

dependent upon the engine revolutions (N) per minute, the total

gear ratio (x) employed, and the radius (R) in feet of the tyres

fitted. The horse-power is a function of the engine torque (T),

the revolutions (N) and the efficiency {n) of the transmission ;

but T and rj vary independently, the former with N and the

latter with both N and x. The general relation between the

engine torque and the tractive effort is expressed by the

equation —

P R = T XT?.

For design purposes, the probable values of R, rj, and the
components of F at the various car speeds, and for N, at which

POWER REQUIREMENTS 79

those speeds are to be attained may be assumed, some factors
being definitely fixed, while others may be expressed in terms of
the speed, the gradient, etc. (see Arts. 50 and 54); but, in
general, all will be, more or less, tentative, and subject to such
adjustments as may be subsequently found to be expedient during
design or on test.

It has been previously statjjBd that the power requirements are
principally dependent upon the tractive resistance and the speed
of the car. But while the former is affected by the latter, the car
speed is entirely determined when the gear ratio, the engine
speed and the size of tyre are settled, since —

y_N^27rR60 NR

X 63360 168x

Hence it is possible, by providing alternative sets of gears, to
so adjust the speed of the car (for any given engine revolutions
and tyre diameter) that the engine torque transmitted to the
road-wheels is equal to the tractive resistances at that speed, and
it is by so doing that manufacturers are able to surmount some
of the difficulties under which they labour, in that bodies varying
greatly in their form, shape, size, weight and carrying capacity are
fitted to almost identically similar chassis, which are to be em-
ployed on roads and in districts that differ considerably in the
character of the gradients encountered, and in the nature of the
road surfaces.

The difficulties above mentioned resulting from the dearth of
data have, however, been largely reduced during recent years>
and many manufacturers have now at their disposal a con-
siderable amount of experimental information relating to engine
torque, road and wind resistances, the efficiency of the trans-
mission gear generally, and the influence of the shape of the
body on the power absorbed, which is proving of great service in
the design of motor vehicles.

48. Accelerometers. — One of the factors that have contributed
to this end is the accelerometer — of which there are several
forms — the Lanchester, the Trotter and the Wimperis instruments
being probably the best known. The first-mentioned is of the
pendulum type, and is described by its inventor in a paper^ on
"Tractive Effort and Acceleration of Automobile Vehicles on

* See Proceedings I,A,E.j Vol. IV.

80 MOTOE CAR ENGINEERING

Land, Air, and Water." In the Wimperis accelerometer,^ a small
framework is mounted upon a vertical spindle, and is supported
so as to be free to rotate in a horizontal plane, its rotation being
controlled by a light spiral hair spring. The framework is so
arranged that its centre of gravity does not coincide with the
axis of rotation, hence any acceleration or deceleration in the
direction of motion of the car causes the heavier side to lag
behind or move forward and partially wind up or unwind the
spring — the amount by which the spring is wound up or
unwound being a measure of the acceleration or retardation.
This is recorded on a suitably graduated scale, over which a
pointer, secured to the axis of the framework, moves, so that the
readings are obtained directly. In order that jolting or vibration
may not affect the accuracy of the readings taken, a small
permanent magnet is incorporated in the instrument to damp
out oscillations from these sources. The accelerometer is com-
pensated so that the readings obtained are for one direction only,
namely, that in which the car is travelling, by meshing the
teeth of two gear wheels, one of which is attached to and mounted
on the axis of the framework, and the other, pivoted on a separate
axis, is fastened to the index pointer. The mass of the first wheel
and the framework and that of the second wheel and a weight
attached thereto are so arranged and disposed that their moments
about their axes are equal, consequently any acceleration at
right angles to the longitudinal axis of the car produces no effect
upon the instrument, since it tends to cause the wheels to rotate
in the same direction, which, being geared together, they are
unable to do.

Mr. Wimperis, in a paper read before the Sheffield meeting of
the British Association in 1910, gives the results of a large
number of observations which he has made with the instrument
in connection with a motor wagon and a heavy touring car
fitted with solid rubber tyres. Among the data tabulated and
graphed are — the indicated and brake horse-powers, the
mechanical efficiency, engine torque and clutch, road and air
resistances. It is also possible to obtain the brake thermal
efficiency, to observe the accelerative properties of an engine,
and to locate the individual losses at particular points of the
transmission.

1 See The Engineer^ 15th Sept., 1910.

POWER REQUIREMENTS

lbs. per ton.
27
30
48
24
3d
45
60

As Mr. Lanchester has stated in his paper, " almost every
new type of vehicle to which the accelerometer is applied
yields up the secrets of its mode of traction, and the weakness
of each particular type, and, in some cases, of each individual
design, is exposed in so graphic a manner as to render very great
help to the designer in effecting desirahle improvements.'*

49. Boad ResiBtance. — From an examination of the nature of
the surface and condition of the roads, it will be obvious that
the road resistance will vary at different places over very wide
limits, and these will depend not only upon the character of the
road surface, but also upon the size and kind of type, the speed
of the car and the method of supporting the frame upon the
axles. In Vol. I., p. 117, the following approximate values are
given : —

Wood blocks dry

Macadamised road hard and dry

Macadamised road bai'd and wet

Macadamised road treated with tar

Asphalte at 60° E.

Flint and gravel, well rolled and dry

Flint and gravel, well rolled and wet

The values quoted apply to pneumatic-tyred vehicles on roads
which are in good condition and have been obtained by comparing
the figures given by several authorities. They may be taken
as representing minimum values, any tendency of the road to
disintegrate causing the resistance to rise immediately. Mr.
Wimperis has found that the resistances may amount to as much
as 250 lbs. per ton on a partly-rolled road and 400 lbs. per ton
on a road which had not been rolled.^

Col. Crompton, M.Inst.C.E., in a paper on "Modern Motor
Vehicles "^ gives the following : —

lbs. per ton.

Boiling and axle resistance of vehicles fitted with pneumatic
tyres on granite, asphalte and wood pavements and on
average macadam in dry weather at all speeds up to 40
miles per hour

Same in wet weather

With solid rubber tyres at speeds up to 15 miles per hour on
asphalte, granite and wood pavement ....

On |2rood macadam dry

On average macadam wet

1 See The Autooav, Feb. 8th, 1913, p. 239.
* « Proceedings Imt C.E., Vol. CLXIX., pp. 2 a $eq.

M.C.B. ^

40
50

50
60
80

82 MOTOR CAR ENGINEERING

In his opinion, it is only on roads which have a soft crnst that
the road resistance of pneumatic-tyred vehicles exceeds 40 lbs.
per ton, and further, that as the hysteresis of the tyre is so small,
the resistance will be, for all practical purposes, the same at all
speeds up to 40 miles per hour.

Mr. Wimperis states that so far as his experiments with
pneumatic tyres have gone, they indicate very little differ-
ence in the magnitude of the road resistances from those
with solid rubber tyres. In the Michelin experiments, however,
the superiority of the pneumatic over the solid tyre was clearly
demonstrated ; and it would appear, that while the latter is
always inferior to the former, the extent of its inferiority
depends very largely upon the nature and condition of the
road surfaces on which they are employed. The method of
supporting the frame upon the axles is of importance as regards
its effect upon the road resistance with unsprung and spring-
supported frames and bodies ; but it is extremely doubtful
whether there is any appreciable variation in the magnitude of
the road resistance with dissimilar systems of springing, except
such as may, possibly, be due to the differences in the ratio of the
unsprung to the total load. Speed would, also, seem to have an
almost negligible effect upon the resistance on good roads under
ordinary touring conditions and at moderate speeds, but on roads
having irregular or undulating surfaces and with racing cars there
may be a considerable increase in the resistance encountered,
owing to shock, the loading of the tyres from the periodic
vibration of the frame on the springs, the effects of tyre slip.

Morin and other experimenters have shown that the road
resistance decreases with an increase in tyre diameter, as is to
be expected, since the area in contact is greater and hence there
is less deformation of the road surface ; while although the work
done in raising a tyre over an obstacle remains unchanged the
duration of the application of the force is greater, and therefore
the force itself is reduced. The results of tests do not, however,
show the same rate of decrease in the resistance, probably because
of the effects produced by various conflicting factors, that it is
impossible to exclude from such tests ; but it is apparently,
approximately, inversely as the square root of the diameter of
the tyre. Thus within the limits of the dimensions usually
manufactured, from 650 mm. to 1,020 mm. — the road resistance

POWER REQUIREMENTS 83

may vary to the extent of about 25 per cent., but with the
diameters ordinarily employed say — 760 mm. to 880 mm. the
variation will probably not exceed 8 per cent., a negligible
quantity, having regard to the fluctuation in the magnitude of the
resistance itself. It is conceivable that the width, shape and
elasticity of the tyre will also have some slight influence upon the
resistance offered by the road.

For design purposes, it is usual to assume that the road resis-
tance approximates to 20 lbs. per ton ('08125 per kilo.) for pneu-
matic tyred vehicles, which, it will be observed, is substantially in
agreement with the values previously given, and hence will form
a sound basis upon which to work.

60. Qradient Besistance. — The tractive effort required to over-
come the resistance due to the gradient is greater generally than
that necessary to overcome either the road or the air. resistance
under normal conditions.

Knowing the weight of the car and the maximum gradient to
be climbed, the tractive effort which must be available at the
road wheels can be accurately determined. Let w be the weight
of the car in pounds, 1 in x the maximum slope of the gradient
in feet and V the speed in miles per hour at which the hill is to
be climbed. Then : —

Distance travelled by car in one minute = -)-**^ — ft.

But X is the distance over which the car moves along the road, when raised
through a vertical height of one unit, so that the horizontal diH])]acenient
will he X cos ^, where B is the angle of inclination of the road.

Height through which car is raised in one minute = ,,^— ,^- -^-. and

tractive effort required = — ^ = .

'■ X cos a Jz'^ _ I

_., , , . . wYx 6,280

Work done per minute = ^^ — . ^

* 60 ^a?a - 1

„ . , wY X 5,280 ^>^

Horse-power required = eo x 33,000 ^f^^^ i

_ 0-0002667 wY
" Jx^ - 1
If V is in metres per second and w is in kilogrammes

The metric horse-power = .

>Jx^ — 1

siQce the metric horse-power or foroe-de-cheyal is equal to 76 metre -kilo-
grammes per second.

84 MOTOR CAR ENGINEERING

For gradients not exceeding 1 in 10, x may be substituted for J^ _ i
without appreciable error.

It will be seen that there are three independent variables — the
weight of the- car, the speed of ascent, and the slope of the hill.
With regard to the first factor, the weight of the chassis in
complete running order can be determined very closely — either
from previous models or by calculation from working drawings,
although the latter is a rather lengthy operation ; but the weight
of the body which may be subsequently fitted and the number of
passengers to be carried are often unknown quantities. Some
license is, however, permissible if two or three alternative sets of
gear ratios are provided, because the speed of the car up the
maximum gradient likely to be encountered may then be made
to closely approximate to that which is desirable for the total
weight of the car when loaded.

The maximum gradient that the car should be capable of
climbing may be taken to be 1 in 4, since cars now are expected
to be able to operate over wide areas, but preferably a 1 in 8^
gradient should be arranged for, as occasionally a standing start
must be made on a steep hill having a high road resistance, while
sharp corners on stiff gradients are not unknown.

51. Air Resistance. — The magnitude of the air resistance
depends upon the velocity of the vehicle relative to the air, and
the shape and extent of the surfaces exposed to \vind pressure.
At low speeds and with bodies of stream-line formation, the power
absorbed in this direction is practically negligible, but it rapidly
rises with an increase in the speed, since the horse-power varies
according to the speed or when wind screens, hoods, etc., are
added. This is due to the disturbance produced in the atmosphere
bv the action of the various forms and surfaces over which the
air passes and it extends in the form of eddy currents not only in
the immediate vicinity of the car but even at some distance from
its path ; whilst with some surfaces, principally those which are
normal to the direction of motion or nearly so, a much reduced
pressure is caused at the back, thus further augmenting the air
resistance. With stream-line bodies, however, the air passes over
them with the minimum of disturbance, as the only factor that
can cause turbulent motion is the skin friction, and this is
extremely small in magnitude at almost any speed compared with
the head resistance of normal surfaces. It must not be assumed,

tOWER REQUIREMENTS 86

however, because of the relative insignificance of air resistance at
normal speeds that the factors upon which it depends may be
disregarded, for any development that tends to reduce the power
required to propel the car is also conducive towards economy,
while the fitting of stream-line bodies greatly contributes to the
lessening of the dust-raising tendencies of the car in high speed
vehicles. Further, it is not too much to say that the high speeds
attained by low-powered cars have only been rendered possible
because of the employment of bodies which ofifer little air resis-
tance. For these reasons the torpedo and stream- line body should
be regarded with favour, especially as the general appearance of
the vehicle is much enhanced by its adoption.

The formula for the total resultant pressure on a thin flat
plate placed normal to a current of free air is ^ : —

p = 0-0032 AV«

where p is the pressure in pounds per square foot, A is the area
in square feet and V is the velocity of the wind in miles per hour.
Dr. T. E. Stanton's earlier experiments^ at the National Physical
Laboratory with flat plates and flat- ended cylinders in an air
channel through which a current of air was flowing at uniform
velocity gave for the former a value of 0*0027 AV^ and for the
latter, with models having ratios of length to diameter ranging
from 1 to 3, to 1 to 6, about 72 per cent, of this. The resultant
air pressure on a flat-ended cylinder in free air should therefore
approximate to (0*72 X 0-0082 AV^) = 00023 AV«.

Mr. C. A. Carus Wilson, M.A., A.M.Inst.C.E., in a paper ^ on
" The Predetermina^^^ion of Train Resistance," quotes from the
Report of the Electric Railway Test Commission at St. Louis in
1904. In the trials made by this Commission, a special car was
constructed, vestibules with different profiles were fitted to the
front and rear, and the pressure on each observed. The profiles
experimented with are shown in Fig. 8 and the data obtained are
given in Table X., columns 2, 3, and 4 for a speed of 60 miles per
liour. Column 5 has been calculated from column 4 and the
pressure recorded for profile No. 3 is taken by Mr. Carus
Wilson as having a mean value between the total pressures for

1 See Proceeding» Inst. C,E., Vol. CLXXI., p. 191.
* See Proceedings Inst. 6*. A'., Vol. CLVJ., pp. 94 et $eq.
» Proceedings Inst. C.E., Vol. CLXXI., p. 227.

MOTOR CAR ENGtNEilRiNG

Nos. 2 and 4. It should be noted that the air pressure constant
for No. 1 profile is of approximately the same value as that just
given for Stanton's experiments on a flat-ended cylinder — 0'0023.

TABLE X.

Pressures on Front and Rear of Car with Various

Profiles.

Profile.

Front
Pressure.

Rear
Suction.

Totel.

ConHtant in
formula
p = k\'i

lbs. per 8q. ft.

lbs. per sq. ft.

llis. persq. ft.

No. 1 (Flat) ....

8-20

0-50

8-70

0-00242

No. 2 (Stmidard) . . .

4-53

1-40

6-93

0-00165

No. 3

4-33

00012

No. 4 (Parabolic) . .

2-60

0-24

2-74

0-00076

No. 6 (Parabolic wedge)

2-10

0-45

2o5

0-00071

The importance of the shape of the ends of a car is very
evident from an inspection of the table and the remarkably small
reduction of pressure on the rear end, with suitable forms, should
be noted. It is probably partly attributable to the effect of its
proximity to the ground, and that as the air, which is under
compression beneath the car passes out behind, it partially
neutralises the reduced pressure existing at the rear. Col. Cromp-
ton observed in the course of the discussion on the paper, that he
believed the results had been confirmed by experiments conducted
by Col. Holden, R.A., on projectiles, although he doubted the
accuracy of the figures quoted for the very short profiles Nos. 4
and 5. It may be remarked, how^ever, that during the experi-
ments made in water at the National Physical Laboratory ^ on a
model of the Lebaudy airship, a region of dead water was
observed to exist at t^e tail end, and it was found that as much
as 13 per cent, of its length could be removed from the tail with-
out appreciably increasing the resistance offered. The sections

» See Engineer, Nov. 15tb, 1912, p. 513.

POWER REQUIREMENTS

shown are taken in the horizontal plane, but it may be assumed
that a further reduction in pressure would be obtained if a simi-
lar section in the vertical plane were
adopted.

So far the air resistance due to the
pressures upon the front and rear ends
of the body has been considered as this
is by far the most important, but in
addition there are the frictional resis-
tances of the sides, the resistance offered
by the mudguards, wheels, axles, etc.,
and the effects produced by the discon-
tinuity of the side, top and bottom sur-
faces of the car. _J L_ 2

52. The skin friction coefficient (f)
for a single surface is expressed by the
ratio between F = one half of the re-
sistance offered by an infinitely thin fiat
plate when placed parallel to the direc-
tion in which the air is fiowing and
the resistance (p) offered by the same
plate when placed normal to the direc-
tion of motion of the air, and hence —

F =^ X p,

Mr. Carus Wilson in the paper pre-
viously referred to stated that the co-
efficient of friction between air and a
fiat surface lies between 0*0025 and
0'0044 depending upon the roughness
of the exposed surface, and that Mr.
Batcheller in the course of some ex-
periments with the pneumatic despatch
tubes of New York found the coefficient
to be 0*0082 for a machined cast iron
surface. Mr. Lanchester gives ^ the
value of fas being from 0*0045 to 0*0075
for smooth plane surfaces of 0*5 to 1*6
square feet area at velocities of from 20

- 4

^ See " Aerodynamics,"' § 167.

Fig. 8.

88 MOTOR CAR ENGINEERING

.to 80 feet per second, while subsequently/ as the result of further
experimental work, he has found that for practical purposes (in
relation to areoplanes) the coeflBcient varies between 005 and
0*16. Hence if the total resistance of a flat surface placed normal
to a current of air, is expressed by the equation — p = 0*0032 VA^,
the air resistance due to skin friction given by these coefScients
will be as follows —

Carus Wilson F = From 0*000008 V«A

to 0-0000141 V«A

Batcheller . F = 0-0000102 V«A

Lanchester (a) F = From 0-0000144 V^A

to 0-000024 V«A

Lanchester (&) F = From 0-000016 V«A

to 0-000048 V«A

Zahm's experiments « indicate that F = 0-0000168 f'^^ Y^'^ per foot of
breadth of surface for smooth surfaces, where I is the length in feet in the
direction of flow and that for rough buckram services F = 0*0000244 V'A.

Thurston,^ for smooth surfaces, has found that

F = 0-0000098 A (V« + 32*32).

It is probable that for such surfaces as are used for car bodies,
whether of the touring or of the racing type, the resistance lies
somewhere between 0*000016 V^A and 0*000024 V"A. It should
be noted that the total resistance with stream-line bodies is only
from 0*25 to 1*5 per cent, of that of normal plane surfaces.

58. The air resistances of the wind screen, mudguards, wheels
and axles are exceedingly difficult to estimate on account of the
nature, character and position of the surfaces presented, as well
as because of the disturbing influence of adjacent bodies upon
the mode of motion of the air. For ordinary purposes, the assump-
tion that they are equivalent to that of a flat plate of equal area
to the frontal projected surface is probably within the limits of
accuracy required. As regards the radiator, some of the air striking
its surface is deflected to the sides and some passes through it,
the resistance of the latter being practically only that due to the
frictional resistance of the cooling surface since the extremely low
velocity of the air passing under the bonnet will cause the head
resistance of any body or surface in that part to be almost, if not

* See '* Aerodynamics," § 247.

■ See Philosophical Magazine^ viii., 1904.

' See Engineering^ Jan. 24th, 1913.

POWER REQUIREMENTS 89

quite negligible. Hence, an estimated resistance of about 50 per
cent, of that due to a flat plate of the same superficial area will
doubtless give a result that will not widely differ from the actual
air resistance offered by the radiator.

The estimation of the effects produced by the discontinuity of
and irregularities in the surfaces exposed to air pressure and by
the shielding of one surface or form by another is also a matter
of great difficulty, as the air deflected from one surface may
either impinge on or entirely escape another; and in all but
exceptional circumstances is incapable of an analytical solution
because of their complexity and the variation in size, form, and
relative positions of the disturbing elements. But it is interesting
to note that Dr. Stanton found ^ the total air resistance of two
plates of the same shape and area when placed at 2*15 diameters
apart to be equivalent to that of a single plate of the same
dimensions, while at 5 diameters apart it amounted to 1*78 of
that of a single plate.

Attempts have been made to derive a formula that will give
the air resistance of a car in terms of the exposed area and the
velocity, which, since it is known that the separate components
of the air resistance are given by equations of the form —

p = constant X area X (velocity)*

should be successful when applied to any particular car ; and as
Dr. Stanton has shown * that the ratio of the wind pressure on a
complicated structure to that on a square board of the same area
is the same as the ratio of the resistance of a small scale model
to that on a small square plane, the air resistance will be pro-
portional to their areas, that is, to the squares of their linear
dimensions for geometrically similar forms. But the projected
areas are difficult to determine with accuracy and there is so
great a diversity in the proportions, dimensions and shapes of
cars and their fittings, that no formula can be indiscriminately
applied, even to cars of the same class.

For simple forms, such as those of racing and some touring
cars, the head resistance and amount of side friction can be fairly
closely approximated to by the use of the data given in the
preceding work, supplemented by such other experimental

1 See Proceedingt Imt, CK, Vol. CLVI.
9 See Proceedings Inst C,E., Vol. CLXXI.

90 MOTOR CAR ENGINEERING

information as to the detailed performances of previous vehicles
as may be at the disposal of the designer. But since there must
always be some element of doubt as to the accuracy of the
constants employed, the sufficiency of the areas taken, and the
assumptions which must always be made where there is any
departure from the original form upon which the data are based,
it is always preferable to obtain the resistance directly from a
closely similar model by the aid of an accelerometer, notwith-
standing the fact that air resistance is a comparatively
unimportant factor at the speeds which are commonly used by
touring cars except when running into a very strong head wind.

54. Air and Road Besistance by means of an Accelerometer. — If
an accelerometer is mounted upon a car in such a manner that
it is incapable of any relative movements, and when the speed at
which the resistance of the car is to be ascertained is attained,
the engine is declutched, the reading on the instrument gives the
retardation produced by the combined air and road resistance
and the frictional resistances, etc., of the transmission up to, and
including, the clutch. The value obtained when the car is
running on the level differs slightly (by about 3 per cent.) from the
true value owing to the momentum stored up in the rotating
parts, and the tests should be made on a gradual downward slope
of, say, from about 1 in 30 to 1 in 60 as then the changes take
place more slowly, thus giving a longer time in which to make
the observations and the effect of the changing rotational
momentum is rendered insignificantly small by comparison. If
the observations made on a series of such tests at different car
speeds and on the different gears are plotted against the velocity,
the laws connecting the total air and road resistance measured at
the clutch for that particular car and the speed of the car can be
determined for each gear. The qualifying words ** measured at
the clutch " are used, because the tractive effort required to over-
come the combined air and road resistances is increased by the
frictional resistances of the transmission, which are not the
same for all gears ; and the actual resistance encountered at the
road wheels will only be rj times the resistance recorded on the
accelerometer. It is the latter, however, which it is desired to
find,, since the engine torque must be sufficient after passing
through the transmission gear to produce a tractive effort equal
to the resistances to be overcome. (See Art. 47.) The relation

POWER REQUIREMENTS 91

between the resistances on the various gears measured at the
clutch will be inversely as the eflBciencies of the transmission.

The total resistance in pounds measured at the clutch is given
by the equation —

FW=/,>W + ci (^)'
and the resistance in lbs. per ton measured at the clutch is —

where fj} = the road resistance in lbs. per ton measured at the
clutch, W is the weight of the car in tons, and c^ is a constant
depending upon the type of the body, etc.

A number of tests were carried out by the Treasury Horse-
power Rating Formula Committee at Brooklands in July, 1912,
to ascertain the relative horse-powers of a number of new and
old cars of various makes, and in tabulating the results it was
assumed that the road resistance was 50 lbs. per ton. It was then
found^ that c^ varied between 5*2 and 10*7 for four-seater cars with
open bodies — hoods were down but some screens were up and
some were not. An average value of c^ was 828 and of k^
was 5*83, on the direct drive.

Therefore —

FJnean = 50 + 5-83 (^) Ibs. per ton.

55. The Efficiency of the Transmission, etc. — The published in-
formation relating to the efficiency of automobile gearing is
exceedingly scanty and it is hardly possible to generalise from
the performances of the various types of gear in other branches
of work, having in view the difference in the conditions under
which they are employed, and because the efficiency depends so
largely upon the mechanical condition of the gear, the effective-
ness of the lubricant and the lubrication, the number of bearings
and the method of their support, the pressures to which the gears
are loaded and the speed at which they are run, while the
presence or absence of any distortion at the bearings, the align-
ment of the shafts, etc., will also influence the transmission
efficiency considerably.

As regards the gearbox, even when on the direct drive, there is

1 See B. A. C. Journal for 26th July and 20th Sept., 1912.

92 MOTOR CAR ENGINEERING

always a certain proportion of the power lost in friction at the
bearings and in churning up the lubricant in the gearbox, which
loss will be the greater as the lubricant becomes more viscous as
the depth of immersion of the wheels is increased. Thus with
grease the eflBciency will be less than with oil ; and if the wheel
teeth just dip into the oil, the efficiency will be greater than if
the oil reaches the level of the bearings. With correctly machine-
cut spur gears, the efficiency of a pair of wheels should reach 96
per cent, when in good condition, and efficiencies of over 98 per
cent, have been attained with a pair of helical gear wheels.
These percentages may be almost regarded as maximum values,
as it is questionable whether they are ever exceeded in actual
practice, especially under light loads and if grease is used.
Under full load, the efficiency may reach 98 per cent, on the
direct drive with oil as the lubricant and about 96 per cent, when
thick grease is used ; while on the indirect, the percentages will
probably seldom be more than 92 and 90 respectively, for the
two lubricants, rising to, say, about 98 and 91 per cent, when
helical teeth are used on the constant mesh wheels. Lower
efficiencies may be anticipated, the longer the gear shifts, and
where the wheels in mesh are nearer to the centres of these shafts,
on account of the effect of flexure upon the tooth action. With
the shaft-to-shaft gearbox the loss will be due to one pair of
wheels only plus churning of bearing losses, so that efficiencies of
about 94 and 92 per cent, for the two lubricants are, probably,
approximately correct.

The Bevel wheels in the rear axle when well finished and in
perfect condition, may have an efficiency almost as high as that
of spur wheels; but it is extremely doubtful if they ever reach so
high a figure, on account of the end thrust upon the bearings,
which is in addition to the usual bearing friction, and because of
the distortion of the wheel teeth which frequently accompanies
the hardening process to which they are subjected, although this
may be, and is sometimes, rectified by grinding the rough cut teeth
to the correct shape after hardening or by the use of special
processes or steels. The accurate meshing of the teeth is also a
matter of some difficulty, since for perfect tooth action the axes
of the two shafts should intersect at the apices of the pitch cones
of the two wheels. Published accounts ^ of experiments carried

^ See Science Ahstracti^ Oct., 1912, p. 479.

POWER REQUIREMENTS 98

oat by Messrs. Waterman and Kenerson in U. S. A. show that
efficiencies of 94*2, 95*1 and 98*9 per cent, are obtainable with
the bevel drive giving a 4'45 to 1 reduction when transmitting 80,
40 and 60 horse-power respectively at 880 revolutions per minute.
These figures were, however, disputed by W. Lanchester in a
letter in the Autocar- relating to his paper ^ on " Worm Gearing,"
on the ground that the dynamometer used was subject to a
possible error of 2 per cent., but this was denied by Mr. Eenerson
in a subsequent letter ^ to the same periodical. It would appear *
that the efficiency at full load can be safely assumed to be about
95 per cent, at higher speeds, say, above 800 revolutions per
minute, and from 94 to 92 per cent, at lower speeds of revolution,
as when on the indirect drive.

The efficiency of worm-gearing, neglecting frictional losses at
the bearings, is to be found from the equation ' : —

tana

tan (a -h a; cp)

where a is the pitch angle of the thread, x is a quantity depend-
ing upon the shape of the thread (being 1*08 for a 29 degrees
thread) and <p is the angle of friction between the worm thread
and wheel tooth, x is usually neglected on account of its small
value, and is due to the fact that the pressure upon the thread
does not act normal to the surfaces in contact. Thus, if op is
very small — as it will be with well lubricated worms which are
not overloaded nor run at too high speeds — rj may reach a high
figure. Within certain limits the efficiency increases slightly
with an increase in rubbing speed.

Professor J. H. Barr gives the following equation for the
efficiency of worms supported in ball thrust bearings : —

__ tan a(l — fi tan a)
"~ tan a + fi

where /x is the coefficient of friction = from 0*02 to 0'04. Actual
efficiency tests indicate, however, that the efficiency of steel
worms with phosphor bronze wheels, when a equals from 30 to
40 degrees, lies somewhere between 87 and 94 per cent., although

1 See Prooeedingt I.A.E., Vol. VII., and Autocar, March 15th, 1912, p. 473.

« See Autocar, May 10th, 1912, p. 865.

5 See Goodman's " Mechanics applied to Engineering."

94 MOTOR CAR ENGINEERING

Messrs . Waterman and Kenerson obtained, in the tests^ above
referred to, efficiencies of between 92*4 and 97'9 per cent, with
an increasing load for the parallel worm ; but these figures are
subject to the remarks made above in connection with the bevel
gear tests.

In the experiments* carried out at the National Physical
Laboratory, it was shown that hollow-faced worms gave
eflSciencies as high as 96*8 per cent, at high speeds under heavy
loads, which is the speed decreased, gradually approached 95 per
cent., the lowest efl&ciency recorded (about 93 per cent.) being
under light load. Differences in the numerical values obtained
will naturally accompany variations in the sizes, proportions and
mechanical perfection and in the tooth clearances of the worms
and wheels, as well as, in the quantity, class and temperature of
the lubricant employed, as was evidenced by these tests. Com-
menting on the results of these tests, Mr. Lanchester points out
that the efficiency at reduced speeds was rarely below 94 percent,
and that it was quite exceptional to record lower efficiencies than
93 per cent., the efficiency being a maximum under heavy loads
at the highest speeds. He claims as a result of similar tests on
the same machine with parallel worms at the Daimler works
that the Hind ley worm is always superior to the parallel worm,
especially under heavy loads, where the efficiency is greater by
from 3 to 4 per cent., and that it can carry loads without a
sacrifice of efficiency which would cause the rupture of the oil film
on parallel worms, latrgely because the oil film between the teeth
of the wheel and the thread of the worm is always well
maintained, that is, within the practical limit of loading.

It will be assumed that the Hindley worm has an efficiency at
least equal to that of bevel gears, namely, 95, 94 and 92 per cent.,
for the three conditions as to speed mentioned above and that
the efficiencies of the parallel type of worm are about 1'5 per
cent, lower than these, namely, 93*5, 92*5 and 90*5 per cent.

Some very high efficiencies have been recorded with silent
chain drives. Mr. A. S. Hill in a paper ^ on " Chains for Power
Transmission " states that the efficiency may range between 94*5
and 98'5 per cent., increasing with the load upon the chain and

» See Science Ahsfractit, Oct., 1912, p. 479.

* See Proceed'vngB I.A.E., Vol. XXll., and Avtooar^ March 15th, 1912, p. 473

8 See Proceeding* l.A.E„ Vol. IV., pp. 314, 315.

POWER REQUIREMENTS

decreasing with the speed at which it is run, and that with well-
designed drives, under average conditions, an efl&ciency of between
94 and 96 per cent, should be maintained. With the lower
figures, therefore, the indirect drive in the gearbox, if chain
driven, should give a combined eflSciency of about 88*5 per cent,
and with the higher, about 92 per cent.

In addition to the losses already referred to, some power is
wasted at the universal joints and at the clutch and its con-
nections, which may be roughly assumed to be about 1 per cfent.
at high speeds, but this will depend upon the angle between the
end shafts, the number of universals fitted, and the condition
of the surfaces. It is probably seldom less than 2 per cent, at
low car-speeds.

TABLE XL

Transmission Efficiency with Spur Gearbox and Bevel or

Worm-drive in Rear Axle.

R^ar Axle Drive.

Gear.

Bevels or Hiiidley Worm.

Parallel Wonn.

Oil.

per cent

920
86o
83-0

87-4
84-7

Grease.

IHT cent.

90-3
83-6
8M

85-5
82-9

Oil.

per cent.

90-6
84-2
81-6

86-0
83-3

Grease.

Return shaft box.
Direct ....
Indirect Higher speeds .
Lower speeds .
Shaft to shaft b&x.

Higher speeds .
Lower speeds .

per cent.

88-9
82 5
79-8

84-2
81-5

This table summarises the efficiencies given in the preceding
text, andy so far as can be ascertained, appears to be comparable
with the results obtained from actual tests. For return shaft
gearboxes where the constant mesh wheels have helical teeth
the efficiencies for the indirect drive may be increased by about
1 per cent. Mr. Legros ^ quotes the results of some experiments
made by Mr. Hess, and recorded in the Motor TradeVy^ during
which, as the load increases, the efficiency rose irregularly from

* See Proceedin^g I,A.E^, Vol. III., pp. 357 and 358.
« See Motor Trader, 25th Sept., 1907, pp. 728-730.

96 MOTOR CAR ENGINEERING

88-1 to 90*7 per cent, on the direct drive, from 86*8 to 87*6 per
cent, on the second speed, and from 82*4 to 84*6 per Cent, on the
bottom gear. On the reverse the efficiency fell from 78*2 per
cent, at light loads to 61'6 per cent, at heavy loads. It is
probable that the quantity and viscosity of the lubricant in the.
gearbox, the variation in the angularity of the propeller shaft
and the differences that must be present in various designs would
am^ly suffice to cause greater deviations in the magnitude of the
efficiencies obtained than are indicated above.

56. The Estimation of Power. — The power developed by the
engine is dissipated in overcoming the resistances to traction
(rolling, gradient and air) and the. frictional losses in the trans-
mission gear between it and the road wheels. These individual
resistances have been examined and values assigned to them,
from which the magnitude of the total resistance can be closely
approximated to at moderate speeds. But under some circum-
stances it is also desired that the power available (that is, at any
given speed, the tractive effort) at the road wheels should be
sufficient to increase the car speed at a certain rate, which should,
however, preferably be not more than three feet per second per
second from considerations of personal comfort and wear and
tear on tyres, etc. This necessitates the expenditure of energy,
the magnitude of which may be found from the contained pro-
duct of the mass of the vehicle, the rate of acceleration and the
distance over which the accelerating force acts ; since the force
required to produce an acceleration equals the mass multiplied
by the acceleration, and the product of this force and the distance
through which the body is moved is the work done, the units
being either lbs., feet, seconds, or G.G.S. Thus, for an accelera-
tion of one foot per second per second, the force required is
2240 -7- 82-2 = 70 lbs. per ton. The force which may be thus
utilised is represented by the difference between the tractive
effort available and the combined air, road and gradient
resistances ; but this force will not be constant, since the engine
torque transmitted varies with the engine revolutions, and as the
car speed increases the tractive resistances become greater, thus
diminishing the available accelerating force, although the aug-
mentation of the resistance at low car speeds may be neglected
for small accelerations.

It will now be clear that the power which it is necessary for

POWER REQUIREMENTS 97

the engine to develop in order to propel the car at a definite
speed under any known conditions of road, gradient, etc., can be
ascertained with reasonable accuracy quite irrespective of the
engine revolutions or the gear-ratios employed. But if the
engine and car speeds are predetermined by other considerations,
the gear<ratios and tyre diameters are at once fixed within
closely defined limits ; and the cylinder dimensions must be such
that the torque transmitted to the road wheels will be, at *any
time, not less than the tractive resistances to be overcome.
Conversely, if the cylinder dimensions and the engine revolutions
are known, the gear ratios, and consequently the car speeds,
must be proportioned so as to equalise the tractive effort trans-
mitted from the engine to the tractive resistances encountered.
(See Art. 47.)

Example, — Find what brake horse-power must be developed
by an engine in order to propel a car weighing 1*5 tons when
fully loaded, up a gradient of 1 in 4 at a speed of 7*5 miles per hour,
if the road resistance is 50 lbs. per ton, and the total air resistance
of a similar vehicle, measured at the clutch on the direct drive

/ V \^
is known to be given by the equation — /« = 5*8 ( -ttt- ) lbs« per

ton.
The tractive effort required in lbs. per ton at the road-wheels is

For road resistance . . . = 60 lbs.

2 240

For gradient resistance = / ^ = 679'1 lbs.

Total . . 629a lbs.

Assuming that the transmission efficiency on the indirect
drive is 82 per cent., the tractive effort required measured at
the clutch to overcome the combined road and gradient resistance
will be —

1-5 X 629-1 -^ 0-82 = 1,160-8 lbs.

The tractive effort measured at the clutch on the direct drive
to overcome the air resistance is given by the equation —

fa = 1-5 X 5-8 (^) = 4-89 lbs.,

but since the car will be on the indirect gear, and the efficiency

M.C.E. H

1)8 . MOTOR CAR ENGINEERING

of the direct drive may be assumed to be 90 per cent., the
tractive effort measured at the clutch will be 4*86 X 0'9 -f-0-82 =
5*37 lbs. This may be neglected for all practical purposes,
as the percentage error involved by so doing is well within
the limits of accuracy demanded or even possible ; but in this
case it will be added to the road and gradient resistances and
the total tractive effort required, F', measured at the clutch, is,
therefore, 1,150-8 + 5-87 = 1,166-17 lbs.
Hence —

_ F' X distance moved in feet per minute
13.H.1.— 38,000

_ 1,156x7-5x5,280
"■ 60 X 33,000
= 2812.

If the car is so geared that it is capable of a speed of 29 miles
per hour on the direct drive, at the same engine speed as that at
which it travels at 7J miles per hour on its bottom gear, the
engine will be able to produce an acceleration of 0*418 feet per
second per second on a gradient of 1 in 40, which may be deter-
mined in the following manner : —

The tractive effort required in lbs. per ton at the road wheels
is —

For road resistance . . . .50 lbs.
For gradient resistance = 2240 -^ 40 = 56 lbs.

106 lbs.

The tractive effort for road and gradient resistances measured
at the clutch will, therefore, amount to 1*5 X 106 -f- 0*9 =
176-7 lbs.

The air resistance, measured at the clutch, at 29 miles per

(29\ ^
YqJ lbs. = 73-2 lbs., and the total tractive effect

for the combined resistances is 176*7 + 78*2 = 249*9 lbs.
The available tractive effect measured at the clutch =

B.H.P. X 83,000 _ 23 jj<j3,OOOj<j50_

Distance moved in feet per min. 29 X 5,280 "" 298*7 li)s.

POWER EEQUIREMENTS 99

Hence force available measured at the clutch for acceleration
purposes = 298-7 — 2499
= 48-8 lbs.

This effort is reduced by transmission through the gearing
to 48*8 X 0*9 = 43'9 lbs., and since for each ton weight an
accelerating force of 70 lbs. is required per 1 foot per second per
second, the rate of acceleration will be 43'9-f-(l'5 X 70) =
0*418 feet per second per second.

CHAPTER V
Determination of Engine Dimensions

57. As has been stated in Art. 47, the dimensions of the engine
may be determined either indirectly, by the power requirements,
or directly, by such considerations as the public demand for an
engine of a certain rated horse-power or cubic capacity, or by .the
desirability of adding to the number of models manufactured. If
the former is the case, the cylinder dimensions that it is
necessary to employ in order to develop sufficient power at the
normal speed of revolution must be calculated ; while, as regards
the latter, the process is reversed, and the horse-power output at
normal engine speed must be ascertained.

A number of formulae have been devised for the purpose of deter-
mining the horse-power in terms of the engine dimensions ; but
these are, in the main, of an empiric character, (though some may
have a rational origin) and therefore, unsuitable for general
adaptation in design. Their utility would appear to be almost
entirely confined to competition work or to estimating the power
for taxation purposes. The assumptions which are commonly
made in connection with the derivation of such formulae neglect
the effects produced by variations in the gas velocities employed,
in the compression ratio, in the stroke-bore ratio and in the cool-
ing surface— cylinder volume ratio; but, while it is admitted
that the influence of these and other factors are often insignifi-
cant within the limits of the dimensions usually employed, and
is sometimes entirely obscured by other causes, of which mixture
strength is one of the most important, their individual tendency
and combined effect cannot be ignored. Hence it is well to start
from first principles excepting where the engines produced by a
manufacturer are of more or less standard design, as then a
formula may be advantageously derived that will give eminently
satisfactory results in that particular works, and perhaps be
applicable to other engines of a similar type and class
elsewhere.

DETERMINATION OF ENGINE* DIMENSIONS 101

58. The Brake HorBe-power in terms of the Engine DimensionB. —

The brake horse-power formula for any engine in terms of the
engine dimensions is :—

7; PLAN n

B.H.P. =

38,000

where 77 is the mechanical efiSciency of the engine, that is, the
ratio between the brake horse-power and the indicated horse-
power and the other terms have their usual significance, namely,
P is the mean effective pressure in pounds per square inch, L is
the length of stroke in feet, A is the area of the piston in square
inches, N is the number of power strokes per minute per cylinder,
and n is the number of cylinders. Thus, t; P is the mean
effective pressure in pounds per square inch of piston area calcu-
lated from the brake horse-power and is a very convenient means
of reference, since the brake horse-power of any engine can be
determined with greater facility and accuracy than the indicated
horse-power and is therefore more frequently known.

If the bore and stroke are in millimetresjbut the remaining terms
have the same meaning as before, the expression for the brake
horse-power becomes—

7?PL'A'Nn

B.H.P. =

649 X 10^

Where metric units are used, the mean effective pressure being
in kilos per mm.^ the bore and stroke in millimetres and N' is
the number of power strokes per second per cylinder, the metric
horse-power may be found from —

Force-de-cheval = " ^^^^' "

and the B.H.P. = yg.OSO

since one brake horse-power =1-014 force-de-cheval, and the
force-de-cheval =75.000 mm. kilos of work per second.

To determine the torque in kilos mm., the B.H.P. should be
multiplied by 76,050 and divided by 2 tt N^

B.H.P. X 76,050

Thus — T in kilos mm. =

27rN'

^ . „ , , B.H.P. X 38,000
T m lbs. feet = ^r~^ — - —

102 • MOTOR ^AK ENGINEERING

69. The Hechanical Efficiency of an Engine depends upon several
factors which may be sammarised under two headings — ^frictional
losses and pumping losses — the former being composed of
mechanical friction at the pistons, bearings and the wearing
surfaces generally ; while the latter is the work done in pumping
the charge into, and exhausting it from, the cylinder. The
principal are : —

(a) The degree of mechauical perfection attained iu the design.

(b) The condition of the working surfaces.

employed.
{(I) The temperature of the cooling water.
(e) The weight of all reciprocating parts.
(/) The speed at which the test is made and the proportion of the fall

load carried by the engine,
(f/) The adequacy of the valve areas and port openings and the

suitability of the valve timing.

The first is of importance because any reduction in the number,
diameter, and rubbing velocity of the working surfaces must con-
duce to a diminution of the frictional losses providing that the
lubrication can be eflfeetively carried out. This should not, how-
ever, be considered as justifying a decrease in the number of the
bearings for the crank and camshafts, as here the provision of a
large number of points of support assists in giving greater
rigidity to the shafts, thus preventing high intensities of pressure
at each end of the journals. For similar reasons, the employ-
ment of overhung rotating shafts carrying radial loads should be
avoided wherever possible. But where a part can be dispensed
with, without impairing the design, it should not be used. One
set of gears can often be arranged to drive the water pump and
the magneto, or the camshaft and the lubricating pump. If
bevels or worms are fitted on the two ends of a shaft, the direc-
tion of motion and the proportions of the gear should be so
arranged that the end thrust from one set is taken up by that
from the other thereby entirely removing or largely reducing the
load upon the thrust bearings that are so often a source of trouble
owing to the diflBculty of providing effective lubrication. It is
not sufficient to neglect these factors because of their small
magnitude. Cams must be correctly shaped, bearing pressures

DETERMINATION OF ENGINE DIMENSIONS 103

kept within certain limits, parts that carry bearings must be
made rigid, and all parts shall be well-proportioned if the highest
efficiency is to be reached.

The condition of the surfaces will affect the mechanical
efficiency because the use of unsuitable materials, bad fitting, or
excessive or inadequate clearances must cause the friction to be
excessive. Further, the supply of lubricant must be copious,
though not excessive, and and it should be of suitable quality in
order to maintain the oil film between the rubbing surfaces,
yet not so viscous as to cause a loss of power in shearing the oil
film.

As regards the cooling water temperature, assuming that all
other variables remain constant, there is some small temperature
range (varying with different engines) over which the most satis-
factory results are obtained. This is probably due to the greater
heat loss and less effective carburation at a lower temperature,
which more than neutralise the advantage to be derived from the
increased weight of the charge taken into the cylinder ; and the
greater frictional losses at the piston at a higher temperature,
while at some still higher temperature, the reduction of the
weight of gas drawn into the cylinder causes the mean effective
pressiure to be diminished, notwithstanding the lower heat loss.
Thus the lower temperature will be conducive to a higher
mechanical efficiency and to a lowering of the mean effective
pressure ; but with a rise of temperature the former will decrease
and the latter become greater, until overheating commences to
take place, and hence, some intermediate temperatures will give
the greatest power output and the most economical consumption of
fuel.

The reduction of the weight of the reciprocating parts to the
minimum value consistent with safety is of importance, especially
for high engine speeds, on account of the high stresses and bearing
loads produced by the inertia forces acting, and which may exceed
those due to the explosion pressure alone unless special attention
is directed to this. In addition, the friction caused by the side thrust
upon the piston from the accelerating and decelerating forces acting
in the line of stroke increases[directly as the reciprocating mass and
as the square of the speed of revolution ; while the power lost in
operating the valve gear, etc., becomes considerably augmented
where heavy parts have to be rapidly set in motion. Speed and

104 MOTOR CAR ENGINEERING

the proportion of the lull load carried by the engine will also
influence the mechanical efficiency, as friction increases with the
speed ; and while some portion of the power lost in overcoming
frictional resistances will vary directly as the load, the friction
losses from inertia loads, and at the piston rings, and the power
required to operate the valves, pumps, magneto, etc., will be almost
entirely independent of the power developed. Hence they will
form a larger proportion of the power under light load than at
full power. Furthermore, the work done in drawing a charge of
gas through a restricted throttle opening will be greater at low
powers than under heavy loads.

Valve and port openings should allow as free an entrance and
exit of the gases as is possible for a high mechanical efficiency,
because the negative work loop of the indicator diagram is
disregarded in ascertaining the indicated horse-power. Thus, if
the pressure during the exhaust is high or during induction it is
low, as they will be if there are restricted valve areas and port
openings, long and indirect passages or badly arranged inlet and
exhaust piping, the area of this loop may be considerable and
thereby diminish the actual power transmitted by a large
amount. Similar remarks apply in some measure to the valve
setting employed, as if this is not correct for the speed at which the
engine is to normally run, both in the timing and in the rate of
opening and closing, having due regard to the extent to which
flexibility and quiet running are desired, there vdll be at some
time a wiredrawing of the charge and hence a diminution in
the quantity of gas taken as well as in the mechanical efficiency.

The mechanical efficiency ranges in practice between about 85
and 90 per cent, at full power, although, at times, values below
the lower limit and sometimes slightly above the higher have
been obtained. For design purposes it is fairly safe to assume a
value approximating to 85 per cent, or perhaps 88 per cent, in
some instances, failing more definite information from the results
of tests with similar engines.

60. The Hean Effective Pressure in the Cylinder is directly
influenced by the compression pressure, for, if the latter is raised,
the former tends to become greater, although the rate of increase
is not the same in both cases. (See Art. 43.) But the diverse
results obtained from engines having the same compression ratio
indicate that there are other factors to be considered of which the

DETERMINATION OF ENGINE DIMENSIONS" 105

most important is the strength of the mixture. An engine may
be adjusted to give the maximum power, highest thermal
efficiency, or most economical results at certain speeds by a
variation in the mixture strength, and this partly accounts for
the differences that exist in engines using the same nominal
compression. Next, as the ratio of the cooling surface to cylinder
volume increases, so does the heat loss to the cooling water, and
therefore the pressures in the cylinder during compression and
expansion, as well as at ignition, will decrease. These will
depend not only upon the shape of the combustion chamber, but
also upon the bore and the ratio of stroke to bore. (See Arts. 40 —
43 and 59.) Whether the effect of these considerations upon the
mean effective pressure is sufficient, or not, to require that notice
should be taken of them, having regard to the marked results
produced by the variations in mixture strength and the gas
velocities employed, is not agreed upon but there is sufficient
evidence to show that their influence is in the directions
indicated, and it wauld be well to make suitable' allowances for
them wherever possible.

For a high mean effective pressure, the valve openings must
have large area, as the compression pressure is dependent upon,
first, the compression ratio ; secondly, upon the extent to which
cooling takes place ; and thirdly, upon the pressure within the
cylinder at the time of closing the inlet valve. Throttling the gases
from any cause or the use of high velocities at high engine speeds
will necessitate a late closing, thus reducing the compression,
and consequently, the mean effective pressure ; while the reten-
tion of the products of combustion from a previous charge in the
cylinder has the tendency to cause over-heating, which still further
reduces the charge weight taken by the engine. As Mr. Pomeroy
expresses it, an engine must have a ** high volumetric efficiency."

The mean effective pressure also depends upon the speed of
revolution or piston speed of the engine and is a maximum at
the speed of maximum torque, which, as previously stated
generally coresponds to a piston speed of about 1,000 to 1,200 feet
per minute (5'0 to 6*0 metres per sec.) or slightly higher for
special engines. This will not be the speed at which the maxi-
mum power is developed as the rate of decrease in the torque,
due to higher gas velocities, will be less than the rate of increase
in the piston speed of the engine. At this speed, the indicated

106 MOTOR CAR ENGINEERING

mean effective pressure generally ranges between 67 and 100 lbs.
per sq. in (0*047 and 0'07 kilos per mm.^) although with engines
built for rating, etc., over 180 lbs. per sq. in. (0*091 kilos per mm.^)
have been attained corresponding to values of rfV of about 57 to
85 lbs. per sq. in. (0*04 to 0*06 kilos per mm.*) and 110 lbs. per
sq. in. (0*077 kilos per mm.*) respectively.

61. Piston Speeds, etc. — The factors influencing the piston speed
revolutions and the ratio of the stroke to bore have been fully
discussed in Arts. 40 — 42, and it is, therefore unnecessary to refer
to them further here. It may, however, be noted that the normal
speed of revolution of the engine, and the ratio of the stroke to
bore, should be largely determined by the speed of maximum
torque and by the nature of the conditions under which the engine
is intended to be employed.

It is difficult to lay down any definite values on account of the
variable effects of the controlling factors, but in Art. 41 the piston
speeds generally obtaining in current practice at the speeds of
maximum torque and maximum power are indicated. These are
principally intended for general guidance, for the ultimate decision
as to what piston speed, revolutions, and stroke bore ratio are to
be employed in a design must be left entirely to the judgment of the
designer, who will no doubt be largely guided by the performances
of previous engines he may haye designed or which are of a similar
type and size, subject to such modifications as the improvements
he proposes to introduce may warrant.

62. Compression Batio. — As has been stated in Art. 43, the
compression ratios generally adopted for engines in touring and
commercial vehicles vary between 3*78 and 4*32 but both higher
and lower values are occasionally employed. The compression
pressures given in that article are the nominal compression
pressures, as although they are calculated from the equation
j>z;Y= constant, it is assumed that the pressure in the cylinder
when the piston is on the out-centre is atmospheric, that com-
pression starts at the commencement of the stroke, and that the
value of 7 is 1*3, and all these assumptions may be incorrect.
The actual compression pressure obtained in an engine having any
given compression ratio will vary with the size of cylinder, the
ratio of cooling surface to compression volume, the speed of the
engine, the velocities of the gases and the pressure in the cylinder
at, and the actual time of closing, the inlet valve.

DETERMINATION OF -ENGINE DIMENSIONS 107

Hence, in order to determine the compression pressure, it is
necessary to estimate the probable value of the exponent r and
the pressure in the cylinder at the time of closing the inlet valve,
from the results obtained during previous tests ; but it is usually
sufficiently accurate, and more convenient, to assume that the
whole of the compression curve follows the law jyv^ = constant,
and not only that for the portion of the stroke completed after
the closing of the inlet valve, since any value that may be
assigned to r is only a mean value. The pressure in the cylinder,
when the inlet valve closes should be approximately that of the
atmosphere. (See also Art. 66.)

68. IThe Cyliiider Dimeiuiioiu required for a stated Horse -power. —
The expressions from which the brake horse-power may be
calculated have been given in Art. 58, and are stated below
in terms of the piston spread as well as the revolutions : —

T^ H P* - '^ ^^^^ ^^ — ^? ^^S n

33,000 ■" 132,000

_ 77 PL^A^N 71 _ V PA^M n

■" 649 X lO'' ~ 2,596 X 10*

ri P'L'A'N' n V FA'M' n

Force-de-cheval =

76,050 " 304-2
75,000 ■" 300

where S is the piston speed in feet per minute, M in metres per
minute and 3/' in metres per second.

Having decided upon the piston speed or the revolutions at
which the required horse-power is to be developed as well as the
stroke-bore ratio, the number of cylinders and the compression
pressure or compression ratio to be employed in the design, the
only unknowns are the mean effective pressure on the brake, and
either the bore or the bore and stroke, according as the piston
speed or the revolutions are fixed.

64. The mean effective pressure may be found in three different
ways.

In all works the results obtained from the various engines
which have undergone test on the bench are recorded, including
the brake horse-power, revolutions and conditions under which
the tests were made and probably, also, particulars of their sub-

108 MOTOR CAR ENGINEERING

sequent performances on the road or on the track after being
fitted to a chassis. These data, particularly the power-speed and
the torque-speed curves, will doubtless have been graphed in order
to render the characteristics of the engine more clearly evident.
From an examination of these, and knowing the general design
of the engines to which the records refer, suitable allowances can
be made for any alterations in the dimensions, construction,
speed, compression, velocities of gases, etc., and the mean effec-
tive pressure which it may be expected will be attained in the
new design can be very closely determined.

This, it need hardly be mentioned, is the most satisfactory
way of working, and should always be resorted to if such figures
are available, even when the changes proposed in the design are
so radical in their character as to render any supposition made
open to doubt as to its probable approximate accuracy, since the
alternative methods given below can only be correct for a par-
ticular set of conditions and the allowance that should be made for
any departure from them depends so much upon the judgment of
the designer for their corrections.

65. The second method is empiric, and suffers from the limita-
tions to which all empirical formulae are subject, namely, that
they are not applicable indiscriminately, but it will be found to
give good average results in its application to engines of from
3 inches (75 mm.) up to about 5 inches (125 mm.) bore, em-
ploying gas velocities of about 6,000 feet per minute (30 metres
per second).

Brake mean effective pressure in lbs. per sq. in. gauge

= kWDVV
where P is the nominal compression pressure in lbs. per

square inch absolute, D is the diameter of cylinder in inches and

k is a constant depending upon the ratio of cooling surface to

combustion chamber volume.

For a low value of this ratio, such as is obtained in cylinders
with valves placed in the head and a high stroke-bore ratio, say,
from 1*6 — 1*8, the value of k approaches 5*6, and for a high value,
as when the valves are arranged on opposite bides of the engine
and a low stroke-bore ratio, say from 1*0 — 1*2, about 5'2. For
present day practice where the valves are all arranged upon one
side of the engine and the stroke-bore ratio is about 1*4, k = 5*45.

If the diameter of the cylinder is in milUmetrjs the constants

DETERMINATION OF ENGINE DIMENSIONS 109

k in the equation become 3*9, 3'65 and 3*76 for the three
conditions given ; and if, in addition, the compression pressure
and the mean effective pressure are in kilos per mm.^ the con-
stants k = 0-0152, 0-014 and 00146 respectively.

It will be observed that in both of these methods the mean
effective pressure on the brake is referred to, as with the former
the indicated horse-power is not always obtainable and as
regards the latter, the expression does not allow of such a refine-
ment as would take account of the small variations in the
mechanical efficiency of engines.

66. The third method may be termed *^ rational," and is some-
what similar to that followed in steam-engine practice. The
general procedure is to ascertain the mean effective pressure
from a theoretical indicator diagram, or from an equation for
the mean effective pressure during adiabatic compression and
expansion — the latter being preferred ; then assume a diagram
factor, and a value for the mechanical efficiency of the engine,
and hence obtain the mean effective pressure on the brake.

The diagram is constructed in the following manner. Since
there must be a reduced pressure in the cylinder to cause the gas
to flow into it, and the inlet valve is maintained open until the
piston has receded some short distance into the cylinder, the
pressure at the end of the stroke will always be below atmo-
spheric. The point at which the compression line will cross the
atmospheric line will depend not only upon these factors but also
upon the engine speed, the velocity of the gases through the
valve, the time of closing the inlet valve, and the ratio of the con-
necting rod to the crank radius. With engines of normal construe-^
tion, employing gas velocities of not more than 7,000 feet per
minute (85 metres per second), this will be sufficiently allowed for
by commencing the compression line at a pressure of from 12*5
to 13 lbs. per square inch (0'88 to 0'91 kilos per cm.^) absolute.
The compression line will follow the law pv"^ = constant where
y ranges from 1*3 to 1*34, being higher for a low surface-
volume ratio, a large bore, or a fast running engine, than for a
high ratio and a slow-speed engine of smaller bore, and should be
taken to the end of the in-stroke. The explosion line should be
drawn vertically at the end of the stroke and rise to a pressure
from 4*0 to 4*2 times the absolute compression, pressure obtained
depending upon the engine speed, the shape of the cylinder, etc..

110 MOTOR CAR ENGINEERING

being nearer to the higher value at moderate speeds and with
cylinders without pockets. The equation of the expansion curve
will be pr"^ = constant, where y is from 1*25 to I'S, and will be
affected by the same considerations as the compression line, but
in a reversed sense, that is, it will be nearer the higher value
when the surface-volume is high. Before drawing these curves,
the compression ratio, r, should be determined as follows : —

and (^ '= i^r

that is - ry = ^^

Then set off unit length OA along the abscissa from the origin
and AB from A equal to r units in length. The length OA
represents the volume of the combustion chamber and AB the
stroke volume of the cylinder, irrespective of the final dimensions.
By taking intermediate points x,y, . . . between A and B, the
pressures at these points can be calculated from the equation
jy^r,> = jj^r^Y (where r^, = OX and Vj, = OB) and plotted on the
diagram. Care should be observed that the pressures are in abso-
lute units and that the volumes are measured from the point 0.

Next, find the mean effective pressure of the diagram, either
with the aid of a planimeter, or by the mid-ordinate method, but
preferably the former, and multiply this by the diagram factor of
0*95 ; the result will be thB indicated mean effective pressure.
The diagram factor is used to compensate for the areas which
will be absent in an actual diagram ; for example, the explosion
pressure will not generally rise to four times the absolute com-
pression pressure, but the line is taken to that point because the
true expansion curve always starts later than the commencement
of the stroke. Similarly, the shapes of the curves are affected
near their termination by the speed of revolution, shape of
cylinder, the exhaust period and the timing of the ignition.

67. The indicated mean effective pressure may also be deter-
mined by calculation in the following manner : —

The work done during the adiabatic expansion of a gas from a
volume t'l to Vi

i-y

DETERMINATION OF ENGINE DIMENSIONS 111

\1— 7 1—7/ 1— 7

_ PiVi—p^t^ «. Pin f i_ 2^\

7 — 1 7—1 \ Pin/

1-7

but ^'

m'2 _. (n\ ^"^

Pin \vj

piv

...Wor.aooe=^{.-©'-)=^(l-;^)

The work done per stroke divided by the displacement of the
piston is the mean effective pressure, and the displacement is
the distance moved times the area of the piston, which equals

Hence — mean effective pressure = . =t7~^ \ (1 — ~;rn)

Pi (i _ A\

■" (7-l)(r-l) V r>-V-

During the compression stroke pi is the compression pressure
and during the expansion stroke ^^i is the ignition pressure, 7
and having their usual significance, namely, the exponent of v in
the equation to the curve of expansion or compression, and the
compression ratio respectively. Hence» making the assumptions
indicated in Art. 66, as regards the pressure at the commence-
ment of compression and the value of 7, the compression
pressure or ratio, whichever is unknown, may be determined, and
from the compression pressure, the pressure at ignition may be
approximated to. Then all the quantities which are required in
order to calculate the mean effective pressure on the compression
and expansion strokes from the above equation are known, and
the difference between the mean effective pressure on the two
strokes, multiplied by the diagram factor, 0*95, will be the mean
effective pressure on the piston.

68. When the indicated mean effective pressure has been
ascertained by either method, it should be multiplied by the
mechanical efficiency in order to determine the brake mean
effective pressure, t;^?, and which, as has been previously stated, may
be assumed to be from 0*85 to 0*88, depending upon the factors
discussed in Art. 59.

This method can be made to give very accurate results, as
with careful discrimination in choosing the constants which are

11-2 MOTOR CAB ENGINEERING

employed, the maximum error need never exceed one per cent.
The aathor has found this to be so in practice ; and it is, there-
fore, very suitable for application to a design where an entirely
new construction is adopted.

69. The only quantities now unknown in the expressions
given in Art. 68 for the brake horse-power are, either (a) the
piston area, or (b) the piston area and the stroke, according as (a)
the piston speed or (b) the engine revolutions, have been
previously decided upon.

. If the piston speed has been specified on substituting for S or
M in the equations, the area of the piston and, consequently,
the cylinder bore may be calculated. The product of the bore
by the stroke-bore ratio will then give the slroke ; and the piston
speed divided by twice the stroke will give the speed of
revolution.

If the engine revolutions at which the engine is to run have
been fixed, on substituting for 2N or 2M in the expression for
the brake horse-power, a quantity, which is the numerical value
of the product of the stroke and the piston area, is obtained ; and
this, if the stroke-bore ratio is represented by .r is equal to
xD X 07854 D* = 0*7854 .rD^ from which the cylinder bore and
the stroke may be determined. The piston speed may then be
found by multiplying the stroke by twice the speed of revolution
or four times the value of N or M.

Some adjustment of the calculated dimensions will probably
be found to be uecessary in order to give even figures, after which
the brake horse-power which the engine will develop should be
determined. This should always be slightly in excess of the
actual power requirements. The speed of revolution or the
piston speed — whichever has been calculated from the design
data — should always be checked, in order to Verify its suitability,
or otherwise, for the work upon which the engine will be engaged,
and if not, such adjustments should be made in the stroke- bore
ratio, revolutions or piston speed as the circumstances demand.

The mode of procedure to be followed when the horse-power
that an engine of definite cylinder dimensions or other specified
data are given will be readily obvious, as it is the converse of
that already outlined, and will therefore require no further
explanation.

.CHAPTER VI

CYLINDERS AND VALVES

7(X Katerial. — Cylinders should be made of hard, close-grained
cast-iron, free from blow-holes, spongy spots, scabs, etc., and
the casting shoald be clean and without warp. It is important
also that the material should be of a homogeneous nature, as the
presence of hard or soft spots causes uneven wear with its harm-
ful effects, and the webbing or finning at one time employed had
a tendency in this direction because of the rapid local cooling
during the solidification of the metal in the mould. Cast-iron is
an excellent material for this purpose, because not only does it
flow freely in the mould, but it soon takes a hard skin surface
that has great wear-resisting capabilities. Where lightness is a
great consideration, cast steel and forged steel have been substi-
tuted, but these metals are inferior to cast-iron for this purpose,
as the former does not admit of the production of such sound
castings and the latter is only suitable for extremely simple
constructions.

Cast or forged steel should never be used where steel pistons
are employed, excepting where the design of piston causes the
rings to take the side thrust, as these materials do not work well
together under the extremely diflScult conditions obtaining in the
cylinder. The welding or rusting up of blow-holes or porous
places should not be permitted in any part of the cylinder
subjected to pressure and should preferably be avoided altogether.
In designing the cylinder it is important to avoid all sharp
corners ; and therefore all flanges, bosses, etc., should be well
filleted and join up to the main casting in well-rounded curves,
especially where great variations in thickness occur, as at the
junction of the jacket with the barrel and in the vicinity of the
valve caps, pads and holding-down flanges.

71. Constniction. — The construction of the cylinders is deter-
mined by (rt) the arrangement of the valves and (6) the number
of cylinders cast together. The valves may be arranged in the

M.C.E. I

114 MOTOR CAR ENGINEERING

cylinder head, all on one side of the engine, or the exhaust on the
one side and the inlet on the opposite side. In the first arrange-
ment, the valves may be arranged vertically, horizontally or vee
fashion. In the second arrangement the valves may be fitted
side by side along the engine, as is now customary, or the inlet
may be placed over the exhaust, the former being either operated
by rocking levers and push rods or of the automatic type. The
cylinders may be cast separately, in pairs, in groups of three,
en bloc or in one with the top half of the crankcase.

The pros and cons of valve • arrangement were discussed in
Vol. I. and may be summarised as follows : —

Valves iH the Head, — (a) Give a good shape to combustion chambers
fi"om the points of view of efficiency and power.

{b) Minimum cooling surface for maximum of capacity.

(d) Valve gear arrangement often defective on account of the use of
rocking levers and long actuating rods, which militate against high
speed.

(e) When inclined at an angle with the axis of the cylinder they are
more expensive to machine.

(/) Completely machined interior when valves are vertical, and
therefore uniform compression, while the polished surface contributes to
a reduction of the heat loss.

(g) Use of valve cages becomes necessary unless the removal of the
valves is to entail dismounting of the cylinder ; and that is generally
some restriction in the valve diameter.

Valves all on one Side. — (a) Cooling surface increased, therefore
greater heat-loss and reduced efficiency.

(6) Pockets contribute to silence by acting as cushions.

(d) Tends to limit diameter of valves unless the cylinders arc spaced
rather widely.

(e) Valve operating gear all on one side makes for facility of
adjustment.

(/) Low cost, compactness and simplicity because of use of one set
of gears and one camshaft.

Valves on Opposite Sides, — (a) Greatest cooling surface per unit of
cylinder capacity.

(b) Pockets contribute to silence by reducing the explosive effect on
ignition.

CYLINDERS AND VALVES 115

(c) Fresh gas does not mix so intimately with residual gases over
exhaust valve, and therefore better combustion can be obtained, or the
engine can be rmi on weaker mixtures.

(rf) Greater control ability.

{e) Permits of valves of the largest dimensions being used.

(/) Two camshafts are necessary, and therefore an increase in
the cost.

With the two last-mentioned arrangements there is often some
difficulty experienced in obtaining a sufficiently small com-
pression volume, especially with high compressions, and ample
cooling spaces round valve chambers underneath the valve,
without undue restriction of passage into cylinder and excessive
cooling surface, when valve openings of large area are employed.
It may be overcome by inclining the valve gear towards the
centre of the cylinder ; but by so doing the cost of machining
the castings is increased, because of the two settings required,
and there is also a tendency to limit the water cooling spaces
near the valve seats. This should be specially guarded against,
on account of the possibility of valves and valve seats becoming
overheated and distorted, thus causing a loss of charge.

When the valves are all on one side, the nuts for securing the
cylinders in position are, sometimes, so placed as to necessitate
the removal of the valves before easy access to them can be
obtained ; and the nuts at the ends of the castings are almost
inaccessible without tiie use of special spanners, through being
crowded too close up to the timing case, the dashboard, or the
fly-wheel, and kept well over the overhanging water jacket. The
adjustment of the valve tappets is, also, frequently a matter of
some difficulty, especially where the end plates for enclosing the
valves are cast integral with the cylinder or the dogs securing
the tappet guides are carried very high up. These points are of
little moment to the manufacturer, but are of vital importance
to an owner-driver or a repairer, who have not the same
resources at their oommand; so that special attention should
be directed to the necessity for accessibility at these parts when
working out the design.

The methods of casting the cylinders have been examined in
Art. 39, and the reader may refer to this for guidance as to the
construction to be adopted. It may be added, however, that

I 2

116 MOTOR CAR ENGINEERING

whatever method in selected, it should be decided upon iu con-
junction with the type of crankshaft and after the bearing areas
required have been determined, on account of the shortening of
the engine produced by the en bloc system. The type of crank-

shaft is important in this respect because the narrowing of the
water space between adjacent cylinders, or its entire absence in
some engines, has the effect of limiting the number and length
of the crankshaft bearings it is possible to arrange for, and the
increase in the shaft diameter necessitated by the reduced length,
in order to provide the requisite bearing areas, is not altogether

CYLINDERS AND VALVES 117

itatisfacliorj, inasmuch aa the same degree of rigidity iu not
attained.

It will be generally found to be adviBable to limit the mono-
block casting for a four-eylinder engine to an 80 mm., say 3| incb,
bore, otherwise the weight of the casting and the difficulty in
handling same wilt more than counterbalance any advantages it
may have in other respects. In some of tlie larger sizes of
engines, the cylinders are cast in pairs (or separately) and then
bolted together so as to form, in eETect, a single casting. The

Pio. 10.— 12-16 h.-p. Sunbeam Engine (1911). .

system is good because it combines the clean compact appear-
ance and rigidity of the en bloc construction with the advantages
of the separate cylinders. The practice, occaBionally followed,
of setting two cylinders so close together that the centre line of
the connecting rod does not coincide with the centre line of the
cylinder, should be avoided, as it either means that the rod must
be heavier, thus increasing the weight of the reciprocating parts,
or a higher stress must be employed in the design, since the
connecting tod is loaded eccentrically and consequently the
crippling load is smaller, ^^en two or more cylinders with

118 MOTOR CAR ENGINEERING

valves on the one side are cast together, it is usual to arrange the
two inlet valves for adjacent cylinders to open into one passage,
which is led to the opposite side of the engine, while in some
designs all four inlet valves open into a common passage. While
this has the effect of causing the casting to be more intricate, it
has the great advantage of allowing complete access to the valves
for examination, assists in producing more effective carburation
and cools the engine, and gives a cleaner appearance to the
engine by reason of the elimination of piping, etc.

If the thermosyphon system of cooling be adopted, the pro-
vision of large water spaces and a good. head of water is impera-
tive for its successful operation, and in all cases the water-passages
around the exhaust valve should be ample, so as to prevent local
distortion. This former is of importance where the induction
pipes pass through the cylinder casting to the opposite side, as
the use of narrow intricate waterways not only restricts the flow
of water, but renders the core liable to damage in casting, and
may result in a large percentage of wasters. Bafies, to direct
the flow of water, because it naturally takes the easiest path,
may with advantage be fitted when both thermosyphon and
pump circulation are used in order to ensure an absence of loc^il
heating, and are especially desirable in mono-block castings where
the water may not flow over all cylinders. The practice some-
times followed of casting the exhaust manifold integral with the
cylinder block is not to be recommended, since overheating will
probably ensue if the engine is run at high loads for any length
of time, although it may be observed that some of the smaller
engines have employed this construction apparently without any
harmful effects asserting themselves ; but apart from this, there
is also the question of the distortion of the cylinder casting
itself and the unknown stress induced thereby to consider. Care
should be taken to see that the shape of the interior of the water
passages is such as will not permit air to be entrapped in any
part, as this would prevent the effective cooling of the cylinder
and cause local overheating.

72. It will be necessary to make provision for sparking plugs,
compression taps, circulating water inlets and outlets, cleaning
holes or doors, bosses, fillets, lugs for holding and bedding down
the covers used for enclosing the valve tappets or perhaps for
carrying the fan bracket, and core-holes. Generally the plugs

i* - -<

CYLINDERS AND VALVES 119

and compression cocks are fitted in the centre of the valve caps,
but occasionally they may be placed either in the centre of the
cylinder head or in the side, the former being preferred, as then
any paraffin or petrol is injected through the cock into the
cylinder itself. In all cases one plug should be placed in each
cylinder as near the inlet valve as practicable, in order that the
spark may take place in a mixture containing but little exhaust
gas. The valve caps should be made of gunmetal so as to
prevent any possibility of rusting up taking place.

The water inlet connection should be placed as low as possible
and so arranged that there is a free flow of water around the
cylinder barrel, while the outlet should be in the vicinity of
the exhaust valve and cause the water to have such a direction of
motion as will bring it over the exhaust valve. Often ihe con-
sideration of other matters renders it impossible to obtain this
desirable arrangement, but it should be aimed at in getting out
the design. The water pipes at top of the cylinder are often
attached to a cast piece which fits over the head of a pair or
block casting, and frequently, in the latter case, the piping is
dispensed with, the cast portion being carried up to the radiator
inlet, where it is reduced to the same size as the radiator connec-
tion. Tbis is a desirable arrangement, since it facilitates
moulding, but every effort should be made to reduce the number
of nuts, etc., required to attach the outlet connection in order to
assist in the easy dismantlement of the engine, such as by
employing studs screwed into the heads or plugs in the heads of
the cylinders, and fitted with blank nuts to prevent leakage past
the thread. If such a construction is employed the cast piece
must be made very substantial, as otherwise there is a difficulty
in preventing leakage at the joint, due to the springing of the
casting.

To render the entrance of the piston as easy as possible, the
bottom edge of the bore should have a slight taper so as to bell-
mouth the part, while to prevent the formation of a ridge at the
upper portion of the cyUnder near the end of the piston travel a
slight recess should be formed, so that the piston will shoot just
beyond the edge. The cylinders should preferably be provided
with some means of keeping them central. This may be arranged
for with separate cylinders, by turning a ring upon the flange
which will fit into a recessed portion of the crankcase, and if

120

MOTOR CAR ENGINEERING

cast ill any other mauner, by fitting a ring which recesset> partly
into the cylinder and partly into the crank-chamber, or by using
two end studs of a larger diameter in the plain part and which is
a good lit into the flange of the cylinders.

78. Thicknesses of Cylinder Walls, etc. — Much of the design of
cylinder thicknesses and proportions is based on experience, hut
can be approached in a rational manner. The combustion
chamber is subject to a bursting stress due to the pressure of
explosion, and as the piston proceeds upon its stroke it exposes

Fig. U, — Sectional EleTation of the 23-30 h.-]

. Argj-Ie Sleeve-viil?e

an increasing portion of the barrel, but to a reduced pressure.
In most engines as now constructed, the parallel portion of the
cylinder is not subjected to the maximum explosion pressure, as
the piston head reaches to the level of valve seatings on the
in-centre, and therefore it need not be of sufficient thickness
to withstand so high a working pressure, but it is safer and
cheaper to make it so in the design.

The ma^cimum explosion pressure to which the cylinder is
subjected may be taken as three-and-a-half times the absolute com-
pression pressure. This pressure is purely nominal on account of
the many factors thnt influence the pressure reached at ignition,

CYLINDERS AND VALVES 121

but it approximates sufficiently closely to, although slightly higher
than, the actual pressures recorded, that for design purposes it
may be assumed to be correct. It should be observed that after
a miss-fire the pressure may rise above the normal value repre-
sented by this ratio but by a very small amount.

Now the size of a casting for a cylinder is such that there
should be no liability to defect from internal stress, if annealing
and resting has been effectively done, neither should there be
any unknown or indeterminate straining actions except those
caused by local distortion from overheating in working, but
which should not be present to any appreciable extent in a
good design. The allowance to be made for wear need only be
small and will probably be covered in the adjustment of the
thickness to even dimensions, while defects in the material itself
are not to be expected in selected castings of good grades of cast-
iron, although cast steel suffers greatly in this respect. The
pressure fluctuates from a maximum to zero and is suddenly
applied, therefore it will be necessaly to use a factor of safety of
from 8 to 10 for cast-iron, and about 15 for cast steel, giving
stresses of from 2,500 to 8,000 per square inch (1*75 to 2*1 kilos
per mm.^ for the former, depending on the grade of material,
and from about 4,000 to 4,500 lbs. per square inch (2*8 to 31
kilos per mm.^) for the latter. It will be found that for smaller
bore cylinders the limiting stress should be somewhat lower values
than these for many parts because of the distortion and some
difficulty in casting that would accompany the use of the thin
shells resulting therefrom.

74. (a) For cylindrical surfaces subjected to pressure the thick-
ness may be obtained from the expression :

where t is the thickness in inches or millimetres, p the maximum

explosive pressure in lbs. per square inch or kilos per mm.^,

D is the diameter in inches or millimetres, and /the permissible

stress at that pressure in lbs. per sq. in. or kilos per mm.^.

Another very good rule, but which can only be applied where

the compression pressure does not exceed 80 lbs. per square inch,

or kilos per mm.^

= 00625 D.

1-22 MOTOR CAR ENGINEERING

75. (b) The thkknest of the cylinder head cannot be calculated
from any formnla for flat or curved plates, since, apart from its
peculiar shape and the uncertainty as to whether the head is
fixed or free at tlie edges, there is usually a core hole through
the centre (the point of maximum stress if free at the edges),
and it is supported against bursting by the contour of the
surface in the vicinity of the valves, the attachment of the jacket,
etc. In current practice it varies from 025" up to 0*35" (6 to
9 mm.)i depending almost entirely upon the size of the cylinder.'

Sectional Elevation
Fig. 12. — 12-16 h.-p. Sunbeam Engine (1913).

If the shape of the cylinder head is truly hemispherical its thick-
ness may be determined from the equation

76. (c) The lower }iart <•/ the cylinder is subjected to a pure
tensile stress due to the vertically upward force at ignition, and
to a tensile stress due to the load upon the piston and its reaction
on the frame and a bending stress due to the side thrust from
the piston and the obliquity of the connecting rod as the piston

CYLINDERS AND VALVEB 123

moves downnards on its stroke. As regaids the latter, the
resultant atr^s, which is generally leae than that from the
former, haa a maximum value near the flange by which it is
attached to the crankcase, and may be considered For the position
of the piston when the crank and the connecting rod are at right
angles on the working stroke. If ii is the ratio of connecting
rod to crank, and r the crank radius at this point in the stroke,
the piston will have moved a dislance r | (n + 1) — Vn* + 1 [,
which nearly equals 0'B8 r for all ratios used in ordinary work.

Sactional End Elevation
Fio. 13.— 12-16 Sunbeam Engine (1913). Cross Section.

The volume V of the cylinder for this position may therefore
be calcuhited, and the pressure will be found from

•{^)"

vhere Pj and V are respectively the absolute explosion pressure
and the volume of the combustion chamber.

124 MOTOR CAR ENGINEERING

The tensile stress /< induced (where D and Di are respectively
the internal and external diameters of the cylinder) is found
from

= ~r^^ -14-7) _ Da(p -14-7)

-J (D*-D») DJ-D»

and D, = V i>''(P.-14-7) +i»

= dV?" ^1^:^+ 1
/

where D and Di are in inches, P is in lbs. per sq. in. absolute
and/, is in lbs. per sq. in.

and = I) yf - 0-01 + 1

where D and Di are in millimetres, P in kilos per mm.* absolute
and ft is in kilos per mm.^

For the tensile stress due to bending, the distance between the
centre of the gudgeon pin and the root of the flange must be
known. Let this be x. This dimension may be readily approxi-
mated to, since the distance between the centre lines of the
gudgeon pin and main bearings is rVn^ + 1, and the distance
between the top of the . crankcase and the centre of the main
bearings is largely determined by the clearance necessary for the
connecting rod and the crank, also the cylinder barrel must be
sufficiently long to eliminate any possibility of the piston
becoming jambed through tilting, or if a scraper ring is fitted to
the skirt of the piston, to keep such a ring within the working
length of the cylinder, when the crank is on the out-centre ; and
the flange thickness generally varies between 0*4 and 0*625 of an

inch (10 and 16 mm.). The side thrust on the cylinder is -j-

(P — 14*7) tan 0, where is the angle between the connecting
rod and line of stroke, so that

tan = ,

Vn^ + 1

CYLINDERS AND VALVES 125

f M
Then from the expression - = ^ the tensile stress produced

7rD«
4

(P -14-7) a;

may be calculated, since M =

It will be found to be simpler to assume an external diameter
for the cylinder, find the stresses due to the load on the piston
and the side thrust due to the obliquity of the connecting rod,
and see that their total is not greater than that permissible for
the material used.

77. The conditions existing at the moment of explosion will,

however (excepting only engines • having abnormally long

cylinders), determine the thickness. Here the upward thrust

ttD^

on the cylinder head is (Pi — 14*7), and this is resisted

by the metal round the cylinder = - (DJ — D^).

Hence, ^ (P^ - 14-7) = ^ (DJ - D V.

D«(Pi - 14-7) = (Df - D^)/e

and Di = dV ^* ^}^'^ +1

Note. — In the preceding work English units have been employed,
but by substituting 0*1 for 14*7, where the latter appears in the text,
the units are converted from the English to the metric system of
measurement as seen above.

78. (d) The width of icater tpaces and the thickness of the jacket
are largely dependent upon practical considerations, as although
the water pressure to which the jacket is tested is from 80 to
40 lbs. per square inch (-021 to '028 kilos per mm.^), it is rather
for the purpose of ascertaining if there are any porous places,
than for ensuring strength. The thickness of the jacket varies
from 0*15 to 0*2 of an inch (8*5 to 5 mm.), about one-twentieth
of the cylinder bore, and the width of water space from 0*5 to
0*75 of an inch (12*5 to 19*5 mm.), about one-sixth of the
cylinder bore. In a few instances, greater water spaces than
the above indicate are employed, but this is sometimes due to

126 MOTOR CAR ENGINEERING

the fact that the manufacturer concerned has two engines fitted
with cylinders which differ, practically, only in the bore, thereby
increasing the width of the water space. The object of this
construction is the reduction of the cost of production by
increasing the number of similar parts manufactured.

Where facings are provided for the attachment of piping or
the fan bracket, the jacket should be thickened up for the
purpose of providing sufficient metal into which the studs may
be screwed, as well as to afford ample strength to resist the
additional load it is called upon to carry. Studs should not
penetrate the water spaces, otherwise it will be impossible to
prevent leakage and ultimately a dirty engine. The water jacket
should preferably be carried down to the level of the top of the
piston when the crank is on the bottom centre.

79. Separate Jackets.— In the foregoing it has been assumed
that the jackets are cast with the cylinders, as is the usual prac-
tice except where lightness assumes special importance. As a
rule they are fitted to cylinders that are of simple construction
and have a long cylindrical portion, although this is not
universally so, as occasionally detachable heads are employed
which carry the valve seats. The jackets may be of, practically,
any sheet metal, but are usually of copper, alaminium or brass ;
and are secured to the main casting by a steel ring shrunk over
the ends, by spinning and caulking, by riveting, screwing or by
clamping, or the joint may be made by means of a rubber ring
which presses inside the cylindrical jacket. All these methods are
rather more expensive than the more conventional construction,
and many of them give rise to trouble through leakage at the joints,
caused by the variation in the expansion of the materials employed
for the cylinder casting and the jacket. It is of the utmost import-
ance, where separate jackets are used, that means should be pro-
vided to take up this difference in the expansion of the two metals,
either by fitting bellows in the wall of the jacket or by the adop-
tion of a construction that will allow of relative movement
between the two parts such as is afforded by the rubber ring
fitted on the Green engine.

80. Sizes of Inlet and Exhaust Ports and Valves. — In order that
the charge taken into the cylinder may be as large as possible, it
is desirable to keep the gas velocities low and the passages as
direct and as free from irregularity and sudden changes in action

CYLINDERS AND VALVES 127

as possible. But large valves set up a considerable amount of
hammering and vibration,
becaoEe of the large mass
to be actuated, and where
the valves are fitted on
one side of the engine,
they are dilfieuU to arrange
for, especially if the stroke-
bore ratio be much more
than, say, 1*5, and the com-
pression ratio is at all high,
while there is a greater
probability of warping tak-
ing place. By staggering
the valve centres, some
increase in the valve dia-
meter may be effected,
and a higher compression
ratio may be employed
without any augmentation
of the ratio of the surface to
the volume of the combus-
tion chamber, by sloping
the centre lines of the
valves towards the centre
of the engine (see Figs. 14
and 15), but both of these
tend to increase the cost
of manufaetiire. The diffi-
culty in regard to the
compression ratio is mostly
experienced in engines
used for special purposes,
where the maximum power
IB required at high engine
speed, and this can only
be attained by the use
of a high compression on

account of the too slow ^^"' H.— Wolseley XaUe and Tnppet Genr.
ignition of the charge under low pressure; and it should

128 MOTOR CAR ENGINEERING

be noted that the quantity of gas taken in by the engine per
stroke diminishes with an increase in speed, although in some
engines the volumetric efficiency is remarkably well maintained
over a wide range of speed, due to the ample size of the inlet
piping employed.

Small valves, on the other hand, necessitating big lifts, intro-
duce undesirable effects from the high velocities and rapid accelera-
tions of the moving parts which thereby become necessary ;
high lifts are also limited, because of the practical limit to the
height of the combustion chamber in which they are placed, and
further, the maximum effective lift that can be given to any valve
is less than one fourth of its diameter. It has, therefore, been
deemed necessary on some racing cars, where Qomparatively high
speeds of revolution and mean effective pressures are essential for
success, to employ two valves for the inlet and for the exhaust
in order to provide sufficient valve area, but the valve friction
may then be increased by from 80 to 40 per cent.

Considerable variations in the gas velocities at normal engine
speed are, however, to be found in ordiijary practice on engines of
the highest class, which is partly due to the beneficial effect of
high gas speeds upon the carburation, but it will generally be
well for the velocity of the gas through the inlet pipe, valves, and
passages to be not greater than 7,000 feet per minute (85*6 metres
per second), and for the exhaust not to exceed 6,000 feet per minute
(80'5 metres per second), at normal engine speed. Mr. Pomeroy,
referring more particularly to racing engines, has stated ^ that '' a
gas velocity of 120 feet per second (86"6 metres per second) is the
maximum compatible with a mean effective pressure of 100 lbs.
per square inch (0*07 kilos per mm.^)." Thus, if the normal piston
speed is 1,200 feet per minute (6*1 meires per second), the area

of the inlet port, Bu will not be less than V ^-^^ D'- = 0*414 D.

7,000

Similarly, the diameter of the exhaust port, Sa = 0"45 D, and clejir

passages should be provided in order that the gas velocities quoted

may not be exceeded. A lower velocity is given to the exhaust

gases in order that the hot products of combustion may be expelled

as soon as possible.

The velocities referred to are the mean gas velocities at normal

engine speed, as at or near the crank position when the piston is

1 Proc. LA.E,, Vol. VI., pp. 81, 82.

CYLINDERS AND VALVES 129

moving at its highest velocity during the stroke (see Fig. 108,
Vol. h)y the gas velocities through the valve and the passages may
be considerably in excess of these, depending largely upon the
rate of opening and the timing of the valves and the inertia of
the gas.

81. As regards the valve areas, it is usual for the lift of the
inlet valve to be made between ^ and ^ of its diameter, and in
order to provide for the interchangeability of the two valves,
which are of the same diameter for the inlet and the exhaust, the
lower velocity through the exhaust valve opening is frequently
obtained by proportionately increasing the lift of the exhaust
valve, although in many cases the same gas velocity is permitted
through both the inlet and exhaust. For a flat valve seat, the
effective area through the valve is irS^, where £3 is the inner
diameter of the valve seating and h is the lift ; but with conical
seated valves, having seats at greater angles than 85 degrees, this
is not so owing to the reduction in the width of the opening by
the interference of the seat in the cylinder. With the usual pro-
portions of valves having seats at an angle of 45 degrees, the nett
area for the flow of the gases is about 12 per cent, less than that
given above for a flat seated valve, and for a 40 degrees valve
seat the area is about 5 per cent. less.

But the reduction of area is dependent upon the relation between
the lift and the width of the valve seat, as well as upon the valve
diameter at the inner edge of the seating, since the effective area
is equal to the curved surface of the frustrum of a cone which has
a base diameter equal to that of the upper edges of the seating
in the cylinder and a top diameter equal to that of the inner
edge of the seating on the valve. For abnormally small lifts
small valve angles and wide seats, the diameter of the base of the
frustrum is, however, reduced to that of the circle drawn through
the point of intersection of a perpendicular drawn from the inner
edge of the valve seating, with the seating in the cylinder. The
effective area past the valve is then the product of the mean of
the circumferences of the two ends of the frustrum and the width
of the opening— the latter being the distance from a point on the
inner edge of the valve seating on the valve to a point on the outer
circumference of the valve seat in the cylinder for the usual
relations of lift and width of seating, that is, the slant height of
the frustrum ; and generally, is the shortest distance between the

M.C.E. K

130 MOTOR CAR ENGINEERING

valve and the seaj;. It is advisable to set out the valve and the seat
in their correct positions where the exact velocities are required,
bat for all ordinary purposes with valves having seats at an angle
of 45 degrees, the effective area may be assumed to be 12 per
cent, less than that calculated from the product of the circumfer-
ence of the inner edge of the valve seat, in the cylinder and the
lift.

Thus, if the lift of the inlet valve is 0*2 of the diameter, the
nominal area will be trBs X 0*2 S3 = 0*2 trBl and the actual area
will approximate to 0*88 X 0*2 TrSf = 0*176 tt^. Then if the
diameter of the cylinder is D, the normal piston speed is 1,200 feet
per minute and the permissible velocity is 7,000 feet per minute.

^ X 1,200 = 0*176 7r8| X 7,000,

and S3 = 0*495 D, say, 0*5 D,
and the lift will be 0*099 D, say, 01 D.

Where the inlet and exhaust valves are made of the same
diameter and the lift of the latter is increased, so as to reduce the
gas velocity, the lift of the exhaust valve will be —

82. Valves are frequently made of steel containing not less
than 25 per cent, of nickel, but often only a 3 or 5 per cent,
nickel steel is used. The valve should have a flat but slightly
rounded head which should join up with the stem in a well-
rounded curve of radius equal to about one-third of the valve
diameter so as to facilitate the flow of gases into and out of the
cylinder by giving a more or less stream-line formation to the
passage ; while such a construction tends to strengthen the valve
at a part where it is subjected to great heat. For very fast-
running engines, it is desirable to reduce the weight of Inetal in
the heads by recessing them slightly on their upper surface.

The valve stems may be made about one-fifth of the valve head
diameter. Valve guides are now made very long, in order to reduce
air leakage when the engine is running throttle down, and arB
often made separate from the cylinder casting of malleable iron
and screwed into the cylinder, or of pressed steel forced into
position, either from the outside or inside. It is for some reasons
preferable, however, for them to be in one with the cylinder, as

CYLINDERS AND VALVES 181

then the possibility of the valves being slightly eccentric with
the valve seats is eliminated; but as with modern methods of
manufacture the liability to this defect is extremely small, and
the renewal of the guides when wear takes place is greatly
facihtated where separate guides are employed, this construction
is generally adopted in current practice. The defect may also
be obviated by fitting the guides into coned recesses, which are
machined at the same time as the valve seats. Occasionally the
lower portion only of the guide is separate from the cylinder,
and is forced into the cylinder. The exhaust valve guide should
come well up the stem of the valve so as to protect it from the
hot gases during exhaust.

It is important that ample cooling spaces should be afforded in
the vicinity of the valve guides and seats, in order to preserve,
as far as possible, a uniform temperature throughout the metal,
and thus minimise the risk of warping, which might result in the
leakage past the valve and jambing in the guides. One of the
possible drawbacks to the overhead type of valve is the difficulty
of effectively cooling these parts, on account of the fact that the
valves are usually supported in cages ; but the latter must not
be dispensed with, since it would then be necessary to remove the
cylinders or at least the heads in order to examine the valves.
See Figs, 4, 7, 8, 10—14 and 16.

Valve seatings need not be abnormally wide, say ^^^ in.
(2*5 mm.) at the most, for tightness depends upon intensity of
pressure and not on the width of seating ; but, at the same time
unduly narrow seatings must not be employed on account of the
facility with which shoulders are then formed upon the valve.
It is common, also, to find the upper edge of the valve seat flush
with the inside of the cylinder, with the result that as wear
through hammering or grinding in takes place the valve areas
become restricted. The valve seat should preferably stand
slightly proud of the surface of the cylinder upon a raised facing
which may be turned off as becomes necessary in course of time.

The angle of the seat is usually 45 degrees, but flatter seatings
have been employed because of the greater area provided by them ;
but the tightness of the valve is assisted by increasing the angle,
there is less probability of foreign substances adhering and the 4t5
degrees angle is easily worked to. Conical seatings are always to
be preferred on account of their self-centering tendency. In

K 2

132 MOTOR CAR ENGINEERING

special designs,inBtead of the seatings being coned, they are carved,
— that in the cylinder being convex and of smaller radius of
curvature than that on the valve which is concave. This con-
struction affords a slightly larger area for any given lift and is
probably tighter than the usual form ; but it would appear to
introduce difficulties as wear takes place, although this is of
no importance in the particular circumstances under which it is
employed, namely, in racing engines.

83. Cylinder Studs or Bolts. — In some engines bolts are
employed to secure the cylinder to the crankcase, whilst in others
studs are used. Where the latter are employed, it is undesirable
to screw them into aluminium, as this metal and its alloys do not
afford a satisfactory fitting, because sooner or later they are apt
to strip the thread or become loose. When it is imperative to
employ studs, it is preferable to screw a threaded bush of brass
or gunmetal into the aluminium, rivet over the ends and
screw the studs into the bush. Bolts are sometimes taken
through to the main bearings, when the design permits of so
doing, and in such cases in order that the taking down of the
main bearings may not loosen the cylinders, a collar should be
formed upon the bolt and recessed into the top of the' crankcase.

The number of bolts employed varies with the method of
casting the cylinders. If separately cast, four bolts or studs
will be fitted ; if cast in pairs, there will be six bolts for each pair ;
if cast in threes, eight bolts, and for an en bloc four-cylinder cast-
ing, either eight or ten bolts. The maximum load upon the
bolts is at the time of ignition, although under some circum-
stances, as, for example, when very long cylinders are employed
and if the bolts or studs are placed abnormally close to the
longitudinal centreline of the engine, the combined effects of the
reaction from the pressure upon the piston and the tilting action
due to the side thrust in the cylinder walls when the crank is
nearly at right angles to the connecting rod, may induce a
stress in the two bolts on the near side of the engine, of greater
magnitude than that from the pressure at ignition. But these
conditions are exceptional and may generally be entirely
neglected.

In a separate cylinder casting, the load is distributed over the
four bolts. With the other methods of casting, when ignition
takes place in one cylinder, the adjacent cylinder may be just

CYLINDERS AND VALVES 138

starting compressing, but the pressure due to the latter can be
disregarded, being of small magnitude at the commencement of
the stroke, so that the load may be taken as attributable to one
cylinder only. Thus, in general, there are four bolts or studs
carrying the load upon the piston at ignition in any one cylinder,
but there may be only three, as, for example, in a four-cylinder
monobloc casting when there are two bolts or studs between each
two cylinders and one bolt or stud at each end of the casting.

The distribution of the load between the bolts or studs will
depend upon their disposition, the proportion of the total load
carried by each being inversely proportional to their distances
from the centre of the cylinder. But within the usual limits of
these dimensions it may be generally assumed that each bolt
or stud carries an equal load at ignition. Thus if n is the
number of studs subject to stress, F is the pressure per unit
area at ignition and D is the diameter of the cylinder —

The maximum load = 7 D^P,

and the load on each bolt = -7- D^P-

The stress in each bolt or stud should not exceed 7,000 lbs. per

square inch for steels usually employed in these parts, and

therefore the area of each bolt or stud of diameter .d at the bottom

of the thread =

TTf? ttD^P

and d =

4u X 7,000
Dn/P

83-6

A reference to Tables XXXL and XXXIIL will give the dia-
meter of the stud or bolt required, according to the standard
thread employed.

CHAPTER VII

VALVE GEARS

84. Importance of a good Valve Gear. — The attention that is
now being directed by manufacturers and others to the design and
improvement of various forms of sleeve, piston, rotary and disc
valves affords ample evidence that the short-comings of the
poppet valve, notably in regard to noise, wear and vibration, and
especially in the modern high speed, small box engine, are clearly
realised. But it must not be imagined that this type of valve
will be quickly superseded, for, at the present time it gives a
marked degree of satisfaction by reason of its simplicity in
operation and comparative freedom from serious trouble (which
is, largely, the result of the ingenuity and skill that has been
concentrated upon its design and construction for many years) ;
and manufacturers are loath to depart from a method that has
proved so successful under the most severe conditions of working,
unless it can be shown that the new construction is in possession
of these essential qualities, and, in addition, has other advantages
to commend it to them, such as, for example, higher efficiency or
power, greater silence, improved working durability, lower cost of
manufacture, less vibration, better appearance, etc. Some or all
of these qualities, in a greater or lesser degree, are claimed for
the kinds of valves mentioned above ; but it is probable, and
reasonable to suppose, that all designs will have to pass through
a stage of development similar to that which the poppet valve
has undergone (though at a more rapid rate on account of the
improved materials which are at hand and the greater experience of
those associated with their design and manufacture), before they
will show their superiority. (See also Vol. I., Arts. 26, 27 and 81.)

On account of the fact that the poppet valve predominates as
largely seen in modern engines and that individual types of valves
require special treatment, the poppet valve design will be more
fully examined.

85. In the production of a good valve mechanism, it is

VALVE GEARS 135

necessary thafc ample areas for the passage of the gases should be
provided as quickly and as silently as possible, with the minimum
amount of wear and vibration. The fulfilment of these conditions
in their entirety is, however, a matter of great difficulty, as
indeed it must be in any mechanism if the opening of the valve
is effected by a cam and the closing by a spring ; but by careful
attention to the design of the cam contours, as well as to other
details, much can be done to eliminate the detrimental effects that
would otherwise assert themselves.

In the first place, the importance of lightness in every part of
the spring-actuated portion of the gear must not be overlooked,
if the engine is to be capable of attaining high 9peed. Heavy
parts cause the whole of the mechanism to be subjected to high
inertia forces during the opening period, and require that
excessively strong springs should be used for their replacement
when closing the valves. For these reasons, the use of long or
heavy tappet rods, rocking levers, etc., should be avoided, as
they are not only harmful in the directions indicated, but also
absorb a large amount of power in operation, and introduce a
number of joints at which wear may take place. When long
rods for the actuating gear are essential they should preferably
be arranged in tension, since this enables a reduction in the mass
to be actuated without impairing the stability of the gear.

Secondly, fewness of parts is desirable, not only because of its
effect in reducing the cost of production and repair, but because
the appearance of the gear is enhanced by the elimination of
superfluous fittings. Thirdly, all parts should, if possible, be
enclosed and self-lubricating, as by so doing trouble from the
accumulation of dirt or absence of oil is obviated ; but care must
be taken to ensure that any part which it may be necessary to
examine in ordinary work is readily accessible, and does not
entail any great amount of dismantlement. The latter point
requires special attention when overhead valves are employed.

86. Valve Timing. — The timing employed in different engines
varies greatly in practice since there are so many influences that
affect the suitability or otherwise of a valve setting for a particular
engine, the principle being the speed of the engine, the area of
the ports, the compression used, and the shape and configuration
of the piping. The last-mentioned factor may cause a slight
adjustment in the setting for each valve to be necessary. The

136 MOTOR CAR ENGINEERING

most expeditious and sure method by means of which the best
setting can be ascertained is by running the engine on the test
bench at the desired speed and taking indicator diagrams from
the cylinders. An examination of the diagrams will reveal
whether the setting of the valves is correct or not, and, incidentally
the correct position at which the ignition may be fixed or the
range of ignition disposed will also ba obtained.

An average setting, suitable for an engine fitted on a touring
car and running at about 1,200 revolutions per minute at normal
speed, is as follows :

Inlet opens 10 degrees late and closes 20 degrees late.
Exhaust opidns 40 degrees early and closes 7 degrees late.

These give periods of 190 degrees and 227 degrees respectively
for the inlet and exhaust valves, which may be taken as repre-
sentative of the majority of settings; and since the camshaft
rotates atone half of the crankshaft speed, the angular displacement
of the camshaft will be 95 degrees and llSj^ degrees. On some
fast-running engines, the times of opening and closing the inlet
valve are delayed by some 5 or 10 degrees, and the exhaust valve
is made to open at about 5 or 10 degrees earlier, primarily in
order to gain a longer time for the expulsion of the exhaust and
the induction of fresh gas, since at high speeds the volumetric
efficiency is probably seldom more than 68 or 70 per cent
Occasionally an overlapping setting of the inlet and the exhaust
is permitted with the idea that the charge of gas taken by the
engine will be increased, on account of the scavenging effect of
the residual gases passing away to the exhaust.

In such cases very little alteration is made in the time quoted
for closing the exhaust, but the inlet valve is caused to open at,
or shortly after, the in-centre. It should be observed, however,
that the same setting will not be equally suitable for touring as
for racing purposes, as if the maximum power is desired, some
sacrifice must be made in the slow-running qualities and in the
flexibility of the engine.

In sleeve valves and other forms of valves which move at the
same angular speed, it should be noted that the width of the port
is only one-half of that due to the travel of the valve, or one
fourth of the movement transmitted by the crankshaft.

In order that the velocity of the gases passing through the
valve may be as uniform as possible it is desirable to obtain the

VALVE GEARS

187

fall openiDg of the valve as early as practicable, but the maximum
piston velocity during the stroke is attained when the crank and
the connecting rod are approximately at right angles, that is,
about 77 degrees after the dead centre with the usual ratio of
connecting rod to crank radius, and where the axis of the
cylinder is directly over the centre of the crankshaft. This gives
a period of opening of from 66 degrees to 70 degrees which is
insufficient to perform the operation quietly and smoothly, and
thus the maximum opening of the inlet valve is often delayed in
touring car engines until from 85 degrees to 90 degrees after top

TABLE XIL

Inlet Valve.

Exhaust Valve.

Operation.

Time.

Crank-
shaft
Period.

Cam-
shaft
Period.

Time.

Crank-

shaft

Period.

Cam-
shaft
Period.

Commences to

open
Full open .

Commences to

close
Closed

10° after
top centre

90° after
top centre

116° after
top centre

20° after
bottom centre

80°
25°
85°

40°

12i°

42i°

40° before
bottom centre

80° after
bottom centre

95° after

bottom centre

7° after

top centre

120°
16°
92°

60°
7J°
46°

centre, and hence the lift is effected during a crankshaft move-
ment of from 75 to 80 degrees. This causes a restriction of the
openings for some portion of the stroke, but is necessary if a
quiet opening is to be obtained. The character of the operation
of clofftng the inlet valves is relatively unimportant from the point
of view of gas velocity, since not only is the piston speed below
its maximum value, but it is also diminishing, and the angle
during which closing has to be effected may be greater. The
exhaust closing period is also of lesser importance than the opening
period as it is essential that the main portion of the spent gases
are expelled as early as possible, but owing to the time available
the difficulties are less pronounced. Still, since the lift of the
exhaust valve is greater than ihat of the inlet valve, a greater
time both for opening and closing the valves is desirable, especially
as manufacturers very frequently use similar springs for inlet
and exhaust valves. The maximum openings of the inlet and

188 MOTOR CAR ENGINEERING

exhaust valves usually take place during the angles of about 25
degrees and 15 degrees of the camshaft respectively, although in
a few engines the exhaust angle has a higher value than these, but
it is seldom possible to make it include the position of maximum
piston speed.

The table on p. 187 summarises the operations of the inlet and
exhaust valves from the foregoing data.

87. Valve Tappets. — Illustrations showing seveiUl examples of
these are given in Vol. I. and in Figs. 5, 7, 10, and 15 of this
book. The construction may be divided into three parts — the
means provided for adjustment, the guide and the cam contact
piece. The adjustment is usually .effected by screwing a set screw
which should be as large diameter as convenient, and fine thread,
into the head of the guide, and fixing it in position either by a
split pin or by a lock-nut. The latter is preferable, since any play
in the thread is taken up, making an extremely rigid fitting.
Very frequently a fibre or hard leather washer is recessed into the
head of the screw, for the purpose of silencing the contact of
tappet with the valve stem.

The guide is employed so that the lift of the valve may be direct
and uninfluenced by the side thrust from the cam. It is desirable
that the guide should be brought down as close to the cam ns
convenient, having regard to the clearance necessary, and in this
respect that shown in Fig. 15 is admirable. The guide should be
of gunmetal and may be secured by screwing, by bolting, or by
the usjB of dogs. In a few designs the foot of the cylinder is
made so that a bush can be inserted, and thus forms the guide.
In this case, it is occasionally arranged so that the removal of
the cylinder removes the tappet gear intact. The length of guide
will in some measure be dependent upon the relative position of
camshaft and the top of crankcase, but it should not be too long,
and it is unwise to make the diameter unduly small in order to
obtain lightness, since bearing surface to take the side thrust is
then sacrificed. It will be generally found that where rollers are
employed, the minimum diameter is determined by the attach-
ment between roller and tappet. Provision should be made to
prevent the rotation of the tappet and roller, although in a
design similar to that shown in Fig. 5, which admits of a very
light construction, it is unnecessary. The contact with the cam
may be made by a roller fitted in the tappet, by the tappet lever.

VALVE GEAES 189

or by forming a collar upon the end of the tappet. Of these, the
first is preferred, on account of the reduction in the friction and
wear on the cam flanks, and is extensively adopted in current work.

The minimum diameter of roller is limited by the diameter of
the pin upon which the roller is fitted, a matter of some import-
ance when the noiseless operation of the gear is considered, but
these must not be made unduly small, as there will otherwise be
some risk of shearing. The form illustrated in Fig. 15 represents
a type frequently employed, which, while providing an inexpensive
construction, has the merit (as has also the design in Fig. 7)
that it can be made with an extremely small radius to the
contact surface for use in conjunction with cams machined solid
with the shaft ; on the other hand, the effect of wear is more
marked. The width of the roller and of the cam varies from
0*3 in. to 0*5 in. (8 to 12 mm.), and the diameter of roller ranges
between 2 and 2*5 times the lift of the valve, but it should be
considered in conjunction with the base diameter of cam and the
character of the opening or closing which it is desired to impart
to the valve. (See next article.) In the design of the details of
the tappet gear, strength and bearing surface are, relatively, of
little importance, the dimensions to be employed being largely
determined by experience. It is, however, of interest to observe
that in Fig. 15, the pressure between the roller and the cam
(neglecting friction) acts along the line XN, and NB is the line
of action of the thrust along the axis of the valve. Hence the
triangle NRX is a triangle of forces— NR = spring load + force
required to open the valve, NX = pressure between the roller and
the cam, and BX represents the tangential force at a radius BO,
which has to be overcome in driving the valve gear at this position.

Supplementary springs of various designs are also frequently
incoi-porated in the tappet head, for the purpose of silencing
the mechanism by maintaining the tappet in contact with the
valve stem and the roller with the cam, but it is doubtful if
these are of very great service, except where strong laminated
springs are employed, since the springs which can be fitted are of
insufficient strength to effectively perform this duty.

88. Cams. — Having ascertained the required valve lift as in
Art. 81, and decided upon the valve setting which is to be
employed, the design of the cam may be proceeded with. When
the arrangement is as seen in Fig. 11, the lift of the cam and

140 MOTOR CAR ENGINEERING

the lift of the valve will be proportional to the respective
distances between the centre line of cam and the centre line
of valve and the axis about which the tappet lever turns. This
tappet lever should be so arranged that the full range of its
movement is divided equally on the two sides of a line passing
through the pivot and at right angles to the axis of the tappet.

The size of a roller or the radius of curvature of tappet to be
used is a question of the relative diameters of the roller and
the cam base — the larger the former, the shorter must be the
period of maximum opening or the longer the period of opening,
for a smooth, quiet movement ; on the other hand, the smaller
the roller, the more pronounced is the wear. A rapid rate of
opening for ordinary work is not so essential as an early
maximum opening, so that it is better for the diameter of
roller to be less than the base of the cam. Where the cams
are solid with the shaft, the bearings for the camshaft are
frequently made by enlarging the shaft and fitting them to
bushed holes in the crankcase, without any means for adjustment.
Further, it is undesirable to have great variations in the diameter
of the shaft at the different points, otherwise the cost of manufac-
ture becomes excessive. Consequently, the maximum distance
between the centre of the shaft and the peak of the cam will to a
large extent be hmited by the diameter of the bearings. When
the cams are separate from the shaft, and keyed or pinned thereto,
there are no definite limits to their dimensions, except those
imposed by convenience and symmetry ; but it will be found to be
desirable to be able to fix the cams permanently on the shaft
before fitting in place. In some cases, the base of the cam is as
small as | in. (22 mm.) diameter, and it may be as large as 2 in.
(50 mm.) diameter, but by far the greater number are between
If in. (85 mm.) and If in. (45 mm.), that is, about five times the
valve lift. The roller or other form of contact is subject to similar
variations in practice, and it is worthy of note that very frequently
it is possible, by carefully drawing out one or two cams to obtain
a shape that not only gives the correct motion but is also easy to
machine. Undercutting of the cams can nearly always be pre-
vented if desired — the exceptional cases being those existing in some
racing engines, where abnormally rapid lifts are given to the valve.

Cams may be divided into two classes — internal and external
— according as the line of contact is on the interior or the exterior

VALVE GEARS 141

of the cam. For motor cycle work, the former is often used, but
for car purposes the latter is universally adopted.

89. The Design of Cams. — In designing a cam, it is desired to
obtain such a shape as will give the desired movement smoothly
and quietly, yet one that will present no exceptional diflScully in
manufacture. In some instances, the motion transmitted is of a
very irregular nature, no pretence being made to produce a good
design, but the evolution of the most efficient shape can be most
expeditiously obtained. There are four definite motions that
may be given to the valve —

(a) Uniform velocity.

{b) Uniform acceleration..

(d) Uniform acceleration and deceleration.

Of these the last-mentioned is preferred, since the velocity of
the parts is uniformly accelerated until half the rise is reached,
and then uniformly decelerated, so that at the point of
maximum opening the velocity is zero. Simple harmonic
motion approximates somewhat to this. With uniform accelera-
tion the velocity increases throughout the rise, and is at
a maximum when the roller reaches the peak of the cam.
Obviously this is undesirable, as it not only gives a restricted
opening during the early and final stages of the movement, but
the parts are travelling at high velocity when the valve reaches
maximum opening, defects to which the first-mentioned motion (a)
is also subject. Thus a cam should be proportioned as indicated
at either (c) and (d). Noise is, of course, directly traceable to the
non-rigid connection between the valve stem and the cam, but
much can be done to eliminate it by good design.

In drawing the cam, the roller, or its equivalent is assumed for
convenience to rotate, and the cam itself to remain stationary.

Taking the data for the exhaust valve given in Table XIL, and
assuming the diameter of base of cam to be 1*5 in., lift 0*4 in.,
clearance 0*003 in., and a roller of 1 in. diameter.

In Fig. 15, OD represents 0*75 in. = radius of cam base,
HE = DM = 0*008 in. = clearance (which may usually be
neglected), EP = AG = BC = 0*4 in. = lift, GM = BE = 0*5 in.
= radius of roller, the angle DOK = 40 degrees = period of
oi)ening, and angle KOL = 12 J degrees = period of maximum
opening, and angle LOJ = 42J degrees = period of closing.

142

MOTOR CAR ENGINEERING

With centre and radii OH, OE, OF, OB, OC draw the arcs of
circles shown. The cam must rise from E to F in turning through
the angle DOK, and fall from F to E in turning through the
angle LOJ. In dealing with cam motions, it is the centre of the
roller that must be considered, and, therefore, the point G must
rise to the point Ag and fall from Qg to P in opening and in
closing the valve respectively.

Fig. 15. — Cam Diagram.

Since the motion given to the reciprocating parts of the valve
gear should be either simple harmonic or as indicated at (c/) above,
the construction to obtain the displacements will be described.

90. Uniform Acceleration and Deceleration. — The acceleration
takes place during the first half of the rise or fall, and the
deceleration during the second half of the rise or fall ; and as
the rate of acceleration or deceleration may be the same during
the two parts of any movement in one direction, it is only

VALVE GEARS 148

necessary to consider one half of the lift. It is obviously possible,
if desired, to give a higher rate of acceleration during the first
portion of the period of opening in order to obtain a larger
valve opening at this time ; whilst the motion may, also, com-
mence and finish with uniform acceleration and deceleration and
have an intermediate period of uniform velocity. The form of
cam necessary in order to impart the latter motion to the valve
is, however, of irregular shape and should not be adopted except
where very quick openings are required.

Dealing with the period of opening, the parts will start with
zero velocity at G (see Fig. 15), reach a maximum velocity at G4
where GG4 is half the lift, and be at zero velocity again at A.

In uniform acceleration, the space passed over in feet is equal
to one half of the acceleration in feet per second, multiplied by
the time in seconds taken to execute the movement, that is,
S = ^at^. Now in ascertaining the vertical displacements of the
roller centre, one of the properties of the parabola is made use
of, namely, that the distance between the foot of the perpendicular
from any point on a parabolic curve to its axis and the apex
of the curve is proportional to the square of the length of that
perpendicular. That is, in Fig. 16b, ab is proportional to pa^,
and therefore ah represents the space passed over, and pa repre-
sents the time taken. Make ab equal to half the lift of the valve,
con struct any parabola, and draw a perpendicular to ab from a,
intersecting the curve in p. Divide pa into the same number of
equal parts as the angle turned through by the camshaft during
one half of the lift is divided into. (Usually it will.be sufficient
to divide this angle into four parts.) Draw parallels to the axis
ab through p^ p^, ps^ and from the points of intersection with the
curve, drop perpendiculars or aby cutting it in ai, og, a^. Then, as
the camshaft is assumed to rotate at uniform angular speed, each
of the divisions of pa represent equal periods of time, and the dis-
tances ftds, ba^f baiy ba will represent the vertical displacements at
the end of four equal and successive movements of the camshaft.

Set oflf along the radial line GA from G (Fig. 15) distances
GGi, GG2, GGs, GG4, . . . equal to fcas, ba^, bai ... and from
A mark AG7 AGe, AG5 equal to ba^, ba^j bai. With as centre,
describe arcs through Gi, G2, Gg, . . . cutting Ai, A2, As, as
shown. Then the points of intersection of the arcs with the
radial lines will represent the relative positions of the centre of

144 MOTOR CAR ENGINEERING

the roller to the cam during the rise. With these points as
centre, and with radius equal to the radius of the roller, describe
the circular arcs shown. The envelope of the curve will be the
shape of the cam for the period of opening. Since EF is the
lift of the valve, an arc through F with as centre will give
the shape of the peak. The flank of the cam for closing may be
obtained in a similar manner, that is, by dividing the angle
during which the valve is closed into (say) eight parts, and con-
taining the arcs through Gi, Gs, Gs, . • . etc., as shown in the
figure. The cam may be completed by drawing internal
tangents to the circles representing the cam base and the roller.

In setting out these cams, it sometimes happens that the arcs
drawn with centres on the radial lines through A6 and A7 cut
away the peak of the cam, and then the arc for full opening
lies outside the envelope of the arcs from A« and A7. In
such cases, some adjustment either of the relative diameters of
the roller and the cam base or of the period of maximum open-
ing must be made ; and it may be pointed out that much can be
done to simplify manufacture, such as by rendering a straight
flank possible, by suitably proportioning the roller to the cam
bases. The lift of the valve for any given angular displacement
is given by the length of the radial line between the circles
through G and the point representing the position of the roller
corresponding to that left. The curve of valve displacement is
shown beneath in Fig. 16.

91. Simple Harmonic Motion. — When a body is moving in a
circular path, the projection of its motion on a diameter i&
termed simple harmonic. Thus, if a semi-circle is drawn with a
diameter equal to the lift of the valve as shown in Fig. 16b, and the
semi-circumference is divided into a number of equal parts, (say)
eight,, the motion of a mass moving along bb^ through the distances
shown during equal periods of time will be simple harmonic.
If therefore the distances GGi, GG2, GGs . . . had been made
equal to bas, baz, &^i, . . . and the centres of the roller circles
had been at the points of intersection of arcs through these
points with the radial lines through Ai, A2, As, . . . the result-
ing cam would have given a simple harmonic motion to. the
valve. The method to be employed when such a motion is
desired is clearly obvious, and should require no further
explanation. It is desirable to draw the cam diagram as well as

VALVE GEARS 145

the coustraction used to obtain the valve displacements at least
four times full size in order to obtain greater accuracy.

92. Valve Spriogs. — The spring is employed to perform the
operation of closing the valve, and if the roller is to make con-
tact with the flank of the cam during the full period, the force
exerted by it must be sufficient to produce the required
acceleration of the valve, tappets, etc., at the highest speed of
revolution at which it is intended that the engine should be run.

For simple harmonic motion, the force required to produce
the acceleration is Mco^r cos d, where M is the reciprocating
mass, 0) is the angular velocity in radians per second, r is the
radius of the crank, and the angle turned through from the
line of stroke. The value of cos reaches its maximum
value when commencing to close the valve, and then ^ =
and cos ^ = 1, so that the expression then becomes Mco^r.
The mass M includes the mass of the whole of the parts
that have a reciprocating motion. The angular velocity
referred to above is not that of the camshaft, but of an equiva-
lent crank which would reciprocate the parts at the desired
speed. Taking the example shown in Fig. 15, the complete
stroke of the gear is effected while the camshaft moves through
42^ degrees so that the angular speed of the equivalent crank

180
is j^ multiplied by the angular speed of the camshaft. Or

180
generally = -g- 0)1, where is the angle turned through by the

camshaft during the period of closing, and c^i is the angular
speed of the camshaft.

Example. — If the weight of the reciprocating mass of valve gear is
1'2 lbs. lift of valve 0*4 in., the revolution of the engine 1,500 per minute,
and the period of closing valve on the camshaft is 42^ degrees, find the
strength of spring to close the valve with a cam having a contour
giving simple harmonic motion.

1-2 /180 X 750 X 2ir\2 02
^*"^ = 32^ ^ V 42^ X 60 ) ^T2
= 68-8 lbs.

For uniform acceleration during the first half of the closing
period and uniform deceleration during the second half, the force
required is found from the fundamental formula s = \ai^ in
the following manner, s = the displacement of the parts in a

M.C.B. L

lbs.

146 MOTOR CAR ENGINEERING

time t seconds, and a is the acceleration required to effect the
movement. The value of t for the data assumed is one half of
the angle of closing divided hy the angle turned through by the
camshaft per second. From the expression the acceleration
may be calculated, and since the force required equals the mass X
acceleration the strength of the spring may be found.

Example. — With the data given in the preceding example, for simple
harmonic motion, find the strength of the spring if the shape of the
cam produces uniform acceleration during the first half of the
period of closing and uniform deceleration during the second half.

12 ~ 2* V360 X 750 j
= 1,500 feet per second.
Force = Mass x Acceleration
_ 1-2 X 1,5 00
"" 32-2
= 65-8 lbs.

The reduction in the strength of the spring from that required
with simple harmonic motion should be noted ; but, whereas the
force required to accelerate the gear is greatest at starting with
S.H.M., the force required for uniform acceleration is required to
act throughout the time of acceleration. It will be obvious
that, if desired, the second half of the valve lift in closing may
be effected in a smaller angular movement of the shaft, thus
giving a larger valve opening, although at the expense of a
stronger spring, and therefore a greater load on the cam and
driving gear. The spring load should be increased by from 20 to
25 per cent, beyond that found above, as the friction at valve stems,
guides, etc., will retard the movement given to the valve.

It will be fully understood that the calculated strength of the
spring is only sufficient up to the speed of revolution assumed,
namely, 1,600 revolutions per minute ; at any higher speed, it
will be unable to accelerate the parts with sufficient rapidity,
consequently the cam will leave the roller and give a later time of
closing, accompanied by shock and noise. Stronger springs, if
used, will cause greater pressure and wear upon the leading flank
of the cam, so that due care must be exercised in selecting the
speed for which the spring is designed.

VALVE GEARS 147

The general method of finding the spring load for any cam is
referred to in pp. 155- and 156.

Having obtained the pressure exerted by the valve spring, the
compression due to the lift of the cam will cause an increase in
this ; the additional load should never exceed 25 per cent.
Unfortunately, however, it is somewhat difficult to use a large
number of coils, which would permit of a big deflection for a very
slight increase in the load, owing to the restricted length avail-
able, so that it is necessary to increase the diameter of the helix.
The number of free coils and the diameter of the helix employed
will therefore require some adjustment by the designer, the
former usually numbering from 8 to 15. The space between the
coils should be such as would permit of at least twice the initial
compression of the spring without the coils coming into contact
with each other.

Example. — To find the proportion of a spring suitable for a load of
60 lbs., the lift of the valve being 0*4 in. Assuming that the mean
diameter of helix is If in., and taking the modulus of rigidity as
13 X 10« (see Arts. 10 to 24), if the permissible stress = 70,000 lbs.
per square inch,

0-39/;

▼ f\.*:

60 X 1|

0-39 X 70,000
= 0145 in.

No. 8 S.W.G. — 0-16 in. is the next largest size of wire, so that this

will be employed, giving a stress of 51,750 lbs. per square inch. It is

probable that No. 9 S.W.G. would be satisfactory, being 0*144 in,

diameter.

8WD3
Deflection per coil = -^ttu

_ 8 X 60 X (!§)»
"■ 13 X 10« x'(0-16)^

= 0*1465 in.

Since the extra compression due to the lift of valve must cot increase
the load by more than 25 per cent., the maximum load must not exceed
75 lbs., and consequently the deflection per coil will therefore not exceed
0*1465x75 ^_«,.
60 ^ 01832 in.

L 2

148 MOTOR CAR ENGINEERING

The product of the number of free coils by the difference in the two
deflections must equal the lift of the valve = 0*4 in., that is —

(0-1832 - 01465) = 0*4

n = 10-9
Say 11 free coils.

93. Valve Oear Arrangements. — The three forms of valve
arrangement have been referred to in Art. 71, and of these, the
second — valves upon one side — is the most extensively employed
because of certain advantages it has over the third form, and
generally also over the overhead type, in regard to appearance
access and cost.

The design of an efficient and simple overhead gear for the
modern high speed engine is not an easy matter unless the means
of ready access to the valve is sacrificed and the disturbance of
the valve timing is not objected to. The only satisfactory gear
of this type is one in which the camshaft is arranged over the
heads of the cylinders, so as to avoid the use of long tappet rods,
and entirely enclosed, so as to ensure adequate lubrication and
the exclusion of dust. These can be easily provided for by
transmitting the drive through a vertical shaft driven by bevels
or worms at each end, but it is in regard to access that the defi-
ciencies are usually apparent, excepting in two or three examples
— the Maudsley and the Green, for instance — as the removal of
the camshaft for the examination of the valves necessitates un-
screwing a number of nuts and resetting the timing gear
when reassembling — operations which are both laborious and
undesirable.

When the valves are placed in pockets at the side or sides the
camshaft may be driven by spur gearing, by screw gearing or by
silent chains, examples of each method being seen in current
practice. With spur-gearing, the teeth may be cut parallel to
the axis of the shaft, or they may be of the helical form, but they
usually have involute teeth. The arrangements employed vary
little — a pinion on the front end of the crankshaft drives a wheel
on the half-time shaft, bat in some cases, because of the great dis-
tance between the camshaft and the crankshaft, and the conse-
quent necessity for wheels of large diameter, the timing gearcase
would assume unduly large proportions ; an intermediate wheel
may then be employed with advantage. Where two camshafts are

VALVE GEAES 149

used, a similar arrangement will be fitted on both sides. Another
shaft is frequentily brought out on one side (Bometimes on both
sides, if tvo camBhafts), and driven by the camshaft wheel for the
purpose of driving the magneto, or pumps, if fitted, the magneto
being disposed at the rear of the liming case, and the pumps, etc.,
either at the front or the rear. The placing of pumps upon the
same shaft as the magneto is desirable, as by so doing a permanent
load is obtained, which tends to ehminate chattering of the
gears owing to variation in the torque requirements of the mag-
neto and the valves. Occasionally the pumps and the magneto
are driven by skew gearing
from the camshaft. This
allows the designer a great
deal of licence in arranging
the parts, and, although rather
more expensive, is to be com-
mended, since the most
convenient and accessible
positions may be selected for
each fitting. It should, how-
ever, be observed that,
generally, the maximum
diameter which the worm can
be made, it placed within the Fio. n
crankcase, is limited by the
diameter of the camshaft bearings. The familiar form of drive
for the magneto and pumps is to arrange a cross-shaft driven
by skew gearing from the camshaft in front of the engine. A
plunger pump can be conveniently operated from the rear end
of the camshaft.

The wheel on the camshaft is often of fibre, clamped by rivets
or screws between gunmetal plates carried by or forming part of
the hub, which is keyed and nutted on to the shaft, but all steel
gunmetal or phosphor bronze may be employed for any of the
timing gears. If, however, fibre is not adopted tor one of the
wheels, it is a common practice to use helical cut gears. Both
fibre and helical Wheels are used tor the purpose of silencing the
gears, and the latter havethe additional advantages in that they are
stronger and have a longer life because a larger number of teeth
are in engagement. Preferably double helical gear wheels should

150 MOTOE CAR ENGINEERING

be employed so as to obviate end thrust, but this greatly in-
creases the coBt of manufacture, and is, therefore, not frequently
adopteii.

The worm gear provides an excellent means for driving the

camshaft as it not only is silent when first fitted but retains this

quality to the end. Fig. 7 shows the arrangement employed on

the 25-h.p. Sheffield-Simplex engine, and in this case the magneto

and oil pump are disposed at the two ends of the shaft Q, which,

it will he seen, is driven by the worm F and drives tlie wheel R

on the camshaft. In some examples a somewhat similar design

is used, a cross-shaft being arranged in front of the engine to

which a worm wheel meshing with a worm on the crankshaft and

a separate worm driving

the camshaft are fitted,

the magneto and pump

being driven as seen in

the figure. This class of

gear is, however, rather

more expensive than the

ordinary spur gear, but

the noiseless operation

more than compensates

Fig. I".— lielsi/e and Crossley Camstiatt for this. It may be noted

Chain Urivea. ^^^^ ^^.j^j^ ^.^^.^ ^^^^.^ ^^^^

has a more marked effect upon the valve setting than with either
spur or chain drive, but this can, o! course, be readily remedied
by adjustment.

Recently, the chain driven camshaft has been introduced by a
number of manufacturers for the purpose of obtaining silence
and because of its successful working in sleeve valve engines, but
the conditions of operation are not analogous, and, therefore, the
question as to the wisdom of the departure from spur and worm
gears must be determined by experience. Undoubtedly, spur gears
do cause noise after longer or shorter periods, on account of the
wear which taken place, but if they are correctly machined and
fitted in the first place, and are made of suitable proportions and
materials, there is little cause for complaint. . Chains are especially
suitable for work where the loads are fairly uniform, aa with sleeve
or rotary valves, and they also provide an easy road to silence, but
since the torque on the camshaft fluctuates considerably any slack

VALVE GEARS 151

•

in the chain will give rise to a severe snatching action that may
prove disasttouB. In order that the driving side of the chain
may be always tight and thus minimise the effects resulting from
the variation in torque, a water pump or a small brake may be
applied to the camshaft. Wear must, however, take place when
two surfaces work together and stretching of the links is also
inevitable, so that the chain will ultimately increase in length
and necessitate the provision of some adjustment to take up the
slack. To prolong the life of gears and to render the time at
which re-setting becomes necessary more remote, it is usual to
use fairly substantial chains. The chain is generally tightened
up either by moving the gear wheels driving the magneto shaft
or by fitting a jockey wheel ; the latter being preferred, notwith-
standing that it involves another bearing since the magneto can
then be clamped rigidly in position. In addition, there should
be means provided for the adjustment of the relative angular
position of the crank and the cam or magneto shafts to compensate
for the altered timing caused by the wear and elongation of the
chain between the driving and the driven shafts. This is some-
times fitted, but in a few cases, the only adjustment embodied in
the design is one for taking up slack, and even this is occasionally
omitted.

The following drives for chain driven camshafts are suggested
by Messrs. The Coventry Chain Co. : —

(1) Single chain from crankshaft to one camshaft.

(2) As No. 1 with chain from camshaft to magneto.

(3) As No. 1 with chain from crankshaft to magneto.

(4) Three-point drive embracing crank, cam and magneto

shafts, the two latter on the same side.

(5) As No. 4 except the cam and magneto shafts are on

opposite sides.

(6) As No. 4 with right and left hand arrangements for two

camshafts.

(7) Combination of Nos. 1 and 4.

(8) No. 1 right and left hand arrangement and magneto driven

by separate chain oflF camshaft.

(9) No. 2 right and left hand arrangement.

(10) Single chain to magneto shaft and from magneto shaft to
overhead camshaft.

152 MOTOR CAR ENGINEERING

There are three principal arrangements of chain drive : —

(a) A three-point drive embracing the crankshaft, camshaft,

and the magneto driving shaft, adjustment being effected
by moving the last mentioned.

(b) A three-point drive embracing two camshafts and the

crankshaft with a jockey wheel tightening arrangement.

from the camshaft (or crankshaft) to the magneto, the
latter generally having some means of adjustment.
With this form of drive it is essential that ample bearing area
is available, and that copious lubrication is provided, since the
pressures on the bearings are far greater than with either spur
or worm gears since the reaction at the bearings is equal to the
pull on the chain.

The design of gearing is dealt with in Chapter XIV.

94. Camshafts. — Camshafts are subjected to combined torsional
and bending stresses— the torsional stress from the transmission
of the torque to the cams and the bending stress owing to the
load on the tappets. They are often supported in bearings
between each cylinder or each pair of cylinders, but the provision
of ample support conduces to efiSciency in operation and is there-
fore desirable. Ball-bearings are sometimes used, but generally
the bearings are simply bronze bushes pegged or secured in place
by set screws and of sufficient diameter to pass over the tops of
the cams, although in some cases this is not so but the bearings
are withdrawn with the shaft. Lubrication is generally effected
by splash from the crankcase, but occasionally a special trough is
provided into which the cams dip.

The material of which the camshaft is made should be -tough,
on account of the severe and suddenly applied loads to which it
is subjected, and hard, so that it may retain a good, smooth surface
at the bearings. A large amount of elongation or ductility is
undesirable, as the large angular movement of the end of the
shaft would cause a not inconsiderable variation in the timing,
especially in a long camshaft. Forged steel of from 85 to 40 tons
ultimate tensile stre3S gives very satisfactory results although
harder and more expensive grades of steel are sometimes used.
Cams, if separate, may be made of a similar quality of steel and
must be thoroughly casehardened on their acting surfaces. They

VALVE GEARS 153

sre either pinned or keyed to the shafli, and it is always wise to
give ample width to the cylindrical portion of the cam as it
greatly assists in fixing the cam square with the shaft when
assembling. It is however preferred that the cams are solid with
the shaft as troubles in adjusting and fixing the cams and the
sheer of the pins are avoided, and the question of renewal after
use is not importunt, since modern steels and methods of case-
hardening have reached so higli a standard of excellence as to
render inequalities in wear eseeedingly remote, so that when a earn
requires replacement it will be necessary to replace all tlie cams.

Fio. 16. — ReDold Comtihaft AdjUBtment.

The load upon the camshaft fluctuates considerably. The
bending moment and the twisting moment upon the shaft are
due to (fl) the compression of the spring, ('/) the force required to
accelerate the reciprocating parts of the valve gear, and (c) the
pressure in the cylinder upon the valve head tending to close the
valve. These have their maximum value during the period of
opening of the exhaust valve and the resultant effect will vary
along the length of the shaft, being greatest near the driving end,
but from considerations of economy in manufacture the shaft is
made the same diameter throughout, excepting, of course, at the
bearings and at the cams. The initial load upon the springs will
be known as well as the extra load due to their compression as
the valves lift, and the pressure in the cylinder can be ascertained
from the indicator diagram or by calculation, but the value of ib)
will depend upon the profile of the cam. Probably the most
satisfactory way of attacking the' general problem for any cam is

154

MOTOR CAR ENGINEERING

by the use of a graphical conBtruction, and this Ti^ill be indicated
by an example.

Supposing that the exhaust valve setting employed in an
engine running at 1,800 revolutions per minute gives a period of
opening on the camshaft of 40 degrees, that the lift is 0*4 in. and
that the motion transmitted to the valve is as shown in Fig. 15,
where OX represents 40 degrees or "00741 second.

Opening Open Closing

i'^^'^ac '**''^^

Y •» -3 S-

-^Z. ^ .2 _S^

Z /5S S

A^ - ■/ ■ X

-3^^-' ^^ X

^ 40*^ '00741 Sec m, !2V «i 42^-00788 Sec -

^— .. . rf «j fS

_2 ^ i^% _ S-^

3^ ^i^ -ei'ksooo- J^Zl 5^

/r V ;Ef" 7 V

y " ^. -. 9 ti «inn/\ J V.

X i./|i :Z- ^^

TT , /=^^ A N

Fig. 19. — Velocity and Acceleration Diagram for Valve Gear.

To draw the Velocity Diagram. — If the velocity of the valve
during opening were uniform the space-time curve would be a
straight line, and if short distances along the curve are considered,
they may be regarded as straight, since the amount of curvature
is small. Therefore, divide the curve into a number of short
lengths, such as AB, and draw the co-ordinates AG, BG. Then
BG is the vertical displacement of the valve effected in a time

represented by AG, and since -^ — = velocity, ^n reprosents

the velocity at that portion of the curve. Now BG in the figure
represents a displacement of '056 in. and AG represents

"00074 second, so that -.^ = ^>^^-. = 75*5 in. per second = 6*8

' AC '00074 ^

VALVE GEABS 155

feet per second, hence, the velocity of the valve for the
portion of the curve considered is 6*3 feet per second. By pro-
ceeding in a similar manner with a sufficient number of lengths
on the curve, and drawing a fair curve through the extremities
of the ordinates set up from OX through the middle point of
AC, a curve of velocity will be obtained similar to that in
Fig. 19.

To draw the Acceleration Diagram. — The acceleration diagram
is obtained from the velocity diagram and the procedure is some-
what similar to that already described. If the velocity of the
valve opening is uniform, the line representing that velocity
would be a horizontal line. Considering the length PQ of the
velocity curve — the velocity at P is 4*5 feet per second, and at
Q it is 6*8 feet per second. Hence, during a period PB =
•000741 second, the velocity has increased by 1*8 feet per

1*8
second, and, therefore, the increase has been at the rate of ^^^„ . ,

•000741

= 2,400 feet per second per second = acceleration. The results

obtained at the various points upon the curve are then plotted,

as before, and the acceleration drawn.

It is advisable to take as short a period of time as possible

consistent with the accurate measurement of distances, wherever

the curvature is at all marked, in order that the error due

to the assumption that AB and PQ are straight lines may be

negligible.

To draw the Load Diagram. — Having found the acceleration
curve, the vertical force required to overcome the inertia of the
valve gear is obtained from the expression — Force = Mass X
Acceleration. Assuming that the reciprocating parts of the valve
mechanism weigh I'l lbs., that the diameter of the valve head is
1*6 in., and that the pressure in the cylinder at exhaust opening
is 40 lbs. per square inch : —

Plot the values of the force found from the above expression
on a camshaft angular displacement base as in Fig. 15. It will
be seen that the maximum accelerating force is at A and amounts
to 114 lbs. The spring load^ for the compression of the spring
in this position will be from 20 to 25 per cent, in excess of this

^ To obtain the exact spring load^ the acceleration diagram should be drawn for
the closing side of the cum since the spring is necessary for closing the valve.

156 MOTOR CAR ENGINEERING

to overcome frictioaal resistances — say that it amounts to
186 lbs. The actual lo&d at any other point will depend upon
the number of free coils, etc., hut it will increase hy about 20 per
cent, and will probably resemble the curve shown in the figure.
The load on the exhaust valve will be represented by the pressure
in the cylinder multiplied by the area of the valve head, and will
diminish in magnitude as is shown. The actual pressures may
be determined from an indicator diagram or may be closely
approximated to by estimation, but the result will differ little
from that plotted in Fig. 20.

These three curves therefore show the vertical loads upon the
camshaft at the exhaust valve from which the curve of resultant
force may be obtained by summation. This reaches a maximum

Datteii ■■ - S.H.M.
Fig. 20. — Load Diagram for Valve Gear.

at the commencement of the opening, as it will generally be, so
that the camshaft is designed for this angle, and any other forces
acting at this time are determined. These are composed of —
(a) Forces acting upon the length of shaft between the same
two bearings as the exhaust valve considered and which
produce a bending moment upon the shaft.
(&) Forces which may act at any point in the shaft which pro-
duce a twisting moment upon the shaft.
It will be found that the forces summarised under (a) for a
four-cylinder engine with valves all on one side, a three bearing
camshaft and fising 1, S, 4, 2 are greatest for Nos. S and 4
cylinders. Here, when No. 8 is approaching the end of the
exhaust stroke, No. 4 is just commencing lo exhaust. Thus,
there will be a pressure acting on the back of the cam equal to

VALVE GEARS 157

the spring load plus the inertia load plus the exhaust pressure load,
since at this portion, of the movement between 20 degrees and 40
degrees before the inner dead centre the parts are being decelerated
and thus will produce a pressure upon the cam. Every case
must be closely examined, as there are so many variables entering
into the question. Only valves which are opening should be
considered, as the pressure of the spring valve does not act upon
the camshaft when the valve is closed and the effect from a
supplementary spring is negligible.

As regards (b) these may be neglected since they are of small
magnitude, excepting in racing engines, and even there they are
not of great value, compared with the high loads due to the rapid
acceleration of the gear.

Taking two cases by way of illustration. Using the data from
which Figs. 19 and 20 have been obtained, and considering a four-
cylinder engine with valves all on one side —

(1) With a three bearing camshaft ;

(2) With a five bearing camshaft.

(1) Assume that the bearings are 10 in. apart and that the
exhaust valves are placed 2 in. from the centre of the
nearest bearing. The load at the opening valve (No. 4) is
340 lbs. and at the closing valve (No. 8) may amount to, say,
200 lbs. The reaction at the end bearing are 40 lbs. from No. 8
and 272 lbs. from No. 4 cylinder = 812 lbs. The greatest bending
moment is at No. 4 exhaust valve.

Then M = fZ

312X2=/X^d«

Since the load is suddenly applied and is alternating, a factor
of safety of 12 should be employed permitting, for 85 tons steel,
a stress of 6,500 lbs. per square inch.

= 0*992 in., say 1 in. diameter.

(2) For a five-bearing shaft only one valve is considered. If
the pitch of bearings is 6 in. and the valve is 2 in. distant
from the centre of one bearing, the reaction at that bearing from
the load of 840 lbs. is 118^ lbs.

168 MOTOE CAE ENGINEEEING

Then M=/Z

113Jx2 = 6,500x^fP

,, ^ ^V ll3^ X 2 X 3'2
6,500 X TT
= 0-71", say 0-76" diameter.

Note. — These must be the minimum diameters employed, if
the shaft is cut for key ways or drilled for pins suitable increases
in the dimensions must be made. It will be observed that the
distances have been measured along the shaft from the centres
of the bearings. This is always the case, as it is assumed that
bending takes place from the centre and not from the edge of a
bearing.

CHAPTER VIII

PISTONS, GUDGEONS AND CONNECTING RODS

95. Material for Piston. — The material most extensirely
employed for the piston is cast iron, on account of its excellent
wearing properties with both cast iron and steel cylinders.
Pressed steel, cast-steel, and malleable cast-iron are sometimes
used, because it is possible to eflfect a reduction in weight on
account of their greater strength; at the same time it must
not be forgotten that pistons made from these metals are much
more expensive, and, therefore, the two questions of extreme
lightness and cost must be considered when deciding the material
to be employed. Further, where either of these metals are
intended for work in conjunction with steel cylinders, special
attention is necessary in regard to the construction employed,
because unless a copious supply of lubricant is maintained, the
surfaces have a tendency to grub up. In some designs of steel
pistons, two wide packing rings of phosphor bronze are fitted,
which if used in steel-cylinders, are so arranged that they take
the side thrust on the piston.

Homogeneity is a desirable quality in the material employed
as the formation of hard spots in the metal leads to ununiform
pressures, and may cause abrasion through overloading and local
heating. The power lost in piston friction represents by far
the greatest fractional loss in the engine.

Piston rings are generally made of a slightly harder grade of
cast iron than that used for the piston, but both steel and phosphor
bronze rings have been successfully employed.

96. Piston Construction. — Pistons may be broadly divided into
three classes — the flat top, the domed top, and the recessed top.
The advantages and disadvantages of these have been discussed
in Vol. I., Art. 16, and need not be referred to here. The upper
portion of the piston is tapped so as to allow for the expansion
of the head due to its higher temperature, the amount allowed
being largely dependent upon the construction followed. For a

160 MOTOR CAR ENGINEERING

domed top the clearance at the top is greater than that for a
flat top, being about three-thousandths of an inch per inch of
diameter for the former to about one and half thousandths per
inch of diameter for the latter. This clearance is gradually
reduced in the body to about one thousandth per inch of diameter.
Webbing is now seldom used to stiffen flat top pistons, but
occasionally concentric rings of metal are formed in the interior
of the piston to assist in cooling the head.

Since the piston serves as a guide for the crosshead as well as
to transmit the pressure in the cylinder to the connecting rod, the
length of the piston should preferably be not less than the
diameter so as to prevent tilting. It varies from I'O to 1*4
times the diameter in current work. For the purpose of
lightening the piston, in some designs a number of holes are
drilled through the skirt, and in others a portion of the piston
is cut away at the sides as may be seen in Figs. 12 and 18,
whilst in many cases the walls are made very thin. Reduction
in weight without the sacrifice of strength is assisted by turning
down the piston to a smaller diameter for about half the length
below the gudgeon pin, although this is done for the purpose
of assisting lubrication by retaining oil between the surfaces.

97. Number and Dimeiuiioiis of Rings. — Considerable variations
are seen in the number of rings employed, as from two to five
rings are to be found in first class work. Usually, either two
or three rings are placed at the top of the piston, and these may
be supplemented by one ring which acts as security for the
gudgeon pin and a scraper ring at the bottom, although in some
racing engines a single ring scarfed at the joint has sufficed to
retain the pressure. The width of the rings averages about ^
of the diameter of the > piston, but slightly wider and also
narrower rings are to be found in practice. It is usual to turn
the rings concentric, but this system is defective since the pressure
is not uniformly distributed around the wall of the cylinder,
although in order to make the ring touch the cylinder throughout
the circumference it is not unusual to turn the rings to a
large diameter, cut them, spring the ends together, and then turn
or grind them to the same diameter as the cylinder. In some
cases the rings are hammered on the inside after cutting instead
of machining.

A few makers make the thickness at the slit less than that

PISTONS, GUDGEONS AND CONNECTING RODS 161

at the part directly opposite it, and Messrs. Willans and Robinson
manufacture a special concentric ring that it is stated will give a
nniform pressure on the cylinder walls. It may be shown ^ that to
obtain this uniformity of pressure, the amount of eccentricity of
the ring should be approximately 0*206 of the thickness of the
ring at its thickest part. Hence a ring of maximum thickness
0*05 D an average value will have an eccentricity of 00103 D
and be about 0*0295 D at the slit. It is not unusual to make the
scraper ring of uniform thickness. ^

The slit in the ring is usually made by a saw cut placed at an
angle of about 45 degrees ; but since the loss of gas takes place
almost entirely at the joint (as is clearly shown when all the slots
work into line) it is preferable to scarf the ring at the joint, and
thus render leakage less likely to take place. The rings should
also be pinned to prevent them working round, but with the thin
bodies now employed this becomes a somewhat difficult matter,
if it is not altogether impossible to effect the purpose with perfect
safety.

98. Piston Thicknesses. — The thickness of the head is largely
dependent upon the judgment of the designer, as if made to the
thickness found by using the ordinary rules for cast iron or steel
plates an unduly heavy piston would result. For flat-topped
pistons without webbing the thickness generally varies from about
0-22 in. (5*5 mm.) to 0*25 in. (6*5 mm.) for a 4 in. (100 mm.)
piston, and from about 0*16 in. (4 mm.) to 0*2 in. (5 mm.) for
a 3 in. (75 mm.) piston. Steel pistons are made even thinner
than the figures here given, as are also those of cast iron in some
engines. Pistons having domed or recessed heads are seldom
made of less thickness than that calculated by the rules given
above for the lower limits (although structurally they are much
stronger) excepting in special cases where a very high speed of
revolution is employed in the engine. Occasionally pistons
are made thinner at the centre of the head than at the
circumference.

The thickness of pistons behind the rings is not subject to
great variations with the range of bores commonly adopted, and
differs little from 0*125 in., or, say, 3 mm. The stress induced
will be found to be small having regard to the high compressive
strength of cast iron. The skirt tapers off from about 0*125 in-

» See Unwin'B " Machine Design "—Part II.
M.C.E. M

162 MOTOK CAR ENGINEERING

(3 mm.) to about 0*09 in. (2*25 mm.) at the lower edge with
cast iron, and to about 0*06 in. (1*6 mm.) with steel pistons.
Where a scraper ring is fitted, it is necessary to thicken up the
piston at the bottom so as to leave about 0*09 in. to 0*06 in. of
metal at the back of the ring.

The bosses for carrying the gudgeon pin are so generally pro-
portioned that the effective length of bearing surface in connect-
ing rod end is from 0*4 to 0*5 of the cylinder bore. The thickness
of metal surrounding the gudgeon pin should not be less at any
point than 0'2 in. (5 mm.) for an 80 mm. piston and 0*25 in.
(6 mm.) for a 100 mm. piston, roughly 0*0625 of the cylinder
bore.

99. Gudgeon Pins. — These should be made either of a very hard
grade of steel or else of a mild steel and thoroughly case-hardened
in order to resist wear, and in addition to permit high loads to
be carried without abrasion.

At one time it was deemed advisable to so place the gudgeon
in the length of the piston that the bearing areas above and
below it were about equal, but now little regard is paid to this.
It is usually arranged between 0*38 and 0*5 of the length of the
piston from its upper edge, the former reducing the height of the
engine, and the latter by removing the gudgeon bearing further
from the piston head conducing to a more efficiently lubricated
part. There is probably insufficient difference in the actual
dimensions to give either any real advantage, and the diameter of
the pin will influence the result.

The pin may be made either solid or hollow. If the former, it
will he necessary to use a small diameter (otherwise the weight
becomes unduly high) and this will probably entail the employ-
ment of greater intensity of bearing pressure. On the other hand,
the adoption of the hollow form although permitting the use of
lower bearing pressures, is at some disadvantage because of the
increase in the weight of the connecting rod end and of the bosses
in the piston. For the solid pin, a very good rule for the diameter
is a minimum of 0*125 of the cylinder bore, and for the hollow
pin a diameter of 0*2 of the cylinder bore. The ratio of the
internal to the external diameter should not exceed 0*66 to 1*0.

The methods employed for securing the pin against rotation
and end movement are many, but the two principal are by a ring
fitted to the piston passing either through or over the ends of the

PISTONS, GUDGEONS AND CONNECTING RODS 163

gudgeon, and by a taper pin screwed into a boss provided on the
piston, the taper portion of the pin fitting into a corresponding
taper in the gudgeon, thus preventing motion in any direction.
Where the former is adopted the ring may be narrow, of cast iron
or of steel, or it may be fairly broad so as to completely cover the
end of the pin, and made either of cast iron or of phosphor bronze ;
but in both constructions means must be provided to prevent
the rotation of the pin. The total length of the pin should be
always less than the cylinder diameter, and of such a dimension
that it cannot make contact with the cylinder wall in any
position.

The gudgeon pin is designed for bearing surface only, as if
suitably proportioned for carrying the load there is ample
strength to resist shear. All bearing areas are calculated by
multiplying the length by the diameter, that is, the area in a
diametral plane, since the greatest intensity of pressure is at
the centre of the bearing. The permissible pressure lies between
1,500 and 2,500 lbs. per sq. in. (1*05 to 1*76 kilos per mm.^)
depending largely upon the form of lubrication provided. For a
fully forced system the higher pressure may be used, but for
splash the lower limit is preferred, and the load is found by
multiplying the pressure at ignition by the cross-sectional area
of the cylinder, as although the inertia load will reduce the
actual load at the faster speeds of rotation, at the slower speeds
the inertia efifect will be small and hence negligible.

100. The Connectiiig Bod. — The material used for this part of
the engine differs with different manufacturers. High strength
carbon steel, nickel steel, and nickel chrome steel, which vary
greatly in their physical characteristics, are all employed, while
occasionally the rods are made of cast steel. This variation in
the grade of steel used does not of necessity indicate the class of
engine produced, but that it is the most suitable, having regard
to the questions of cost, manufacturing facilities, speed of engine,
power, etc.

The length of the connecting rod is. made between 4*0 and 5*0
times the length of the crank, but the majority of makers keep
within a ratio of 4*5 to 4*75 to 1. It is desirable to make the
connecting rod as long as possible, but limitations are imposed
by the height of engine which is practicable, and with longstroke
engines, unless an abnormally high engine is to result, the con-

M 2

164 MOTOR CAR ENGINEERING

necting rod must be kept down to nearer the lower limit given.
In some special cases the ratio of connecting rod to crank is even
less than 4*0. To. obtain the strongest section to resist the
bending load on the rod, the H section is commonly employed,
although the hollow circular rod has some adherents. The
former is generally drop forged, and comparatively little machine
work is done upon it except at the ends, but where light-
ness and uniformity of weight are of the highest importance
the rod is often machined all over. With the circular rod, this
is forged and turned throughout its length, and in most cases
the hole through its centre serves as a duct to carry oil to the
small end. On account of the little movement at the gudgeon
pin, and the class of materials employed, it is unnecessary to
make this end adjustable. It is also undesirable, because of the
increase in weight which it would necessitate. The bottom end
is, however, arranged so that adjustments may be eflfected there.

101. Load upon the Rod. — The load upon the rod is of two kinds
— the end load due to the pressure upon the piston, and the
inertia load due to the swaying on the rod. The former is a
maximum when the latter is at its minimum, namely, on the
inner dead centre, and decreases as expansion takes place. The
transverse inertia load increases as the crank moves from the
dead centre, and is at its maximum when the crank is nearly
at right angles to the connecting rod — the actual position will
depend upon the ratio of connecting rod to crank radius, but
may be assumed to be in the position stated without tangible
error. Now, both these loads must be considered in the design
of the rod, especially the latter, which often produces a stress in
excess of that from the former.

In the design, the end load on the rod is taken to be the full
pressure upon the piston, since the maximum load will occur at
starting up and when running at low speed, and the inertia
effects are then negligible. For the position of maximum trans-
verse bending force on the rod, the end load is taken to be to
that on the piston only (the inertia force in the line of stroke has
here disappeared), and the eflfect of obliquity is neglected. That
no substantial error is introduced may be readily proved.
Referring to Fig. 21, the forces acting at the gudgeon pin are —
P, the pressure on the piston ; B, the thrust on the cylinder
wall ; and S, the thrust^ along the connecting rod. The value

PISTONS, GUDGEONS AND CONNECTING RODS 166

of S is F sec. 0^ and sec. is greatest when is greatest, that is
when the crank and connecting rod are at right angles. In the
figure, considering the triangle OCX, sec. =

nr n n

When n = 4*5, S = P ^^\^ ^ = 1'024 P ; that is, by taking

the load on the rod as P, the error is only 2*4 per cent.

102. The Design of the Bod. — The design of the connecting rod
is in three parts : —

(1) The npper part of the rod and attachment to gudgeon

pin.

(2) The body of the rod.

(3) The attachment to the crank.

The attachment to the gudgeon pin will be largely determined
by the length and diameter of the pin. Usually this end is fitted
with a hardened steel bush, which projects slightly beyond the
small end of the rod on each side, but phosphor bronze and hard
gunmetal bushes are also fitted. Means for lubrication must be
provided, and these will consist of a hole or cup formed in the
extreme end of the rod in the case of splash lubrication, and a
pipe led to the underside of the pin in the case of forced lubrica-
tion. Provision must be made to prevent the rotation of the
bush, and preferably there should be a recess cut in either the
outside of the bush or the inside of the hole into which it is
fitted so that the maintenance of the supply of lubricant may be
ensured. From strength considerations it will be generally
found there is ample metal in the small end, and it is there-
fore only necessary to point out that it is essential that good
radii are provided between the small end and its junction with
the upper part of the rod.

The upper part of the rod near the end is treated as subject to

PttD*

direct stress. The load is — j— where P is the explosion pres-
sure and D is the diameter of the cylinder, so that the cross-sectional
area required is — ^ r-/. It is therefore only necessary to

choose a section for the rod which has the required area. For
hoUow circular rods it is inadvisable for the internal diameter to

166 MOTOR CAR ENGINEERING

exceed 0*65 of the external diameter, bat it is generally best to
leave the determination of the exact dimensions for this part of
all rods until after those for the body have been settled.

The Body of the Rod. — The connecting rod must be considered
in two positions : —

(a) On the inner dead centre.

{b) When at right angles to the crank.

(a) Here the connecting rod is a column hinged at both ends,
since bending will take place in the plane of reciprocation, to
which Gordon's formula may be applied.

P /^

. Then±=-— -?

A 1 + «p
F is the load upon the piston at ignition. A is the cross- sectional

area at the middle of the rod. a = q-tw^ (see Art. 14), 1 =

length of the connecting rod. k is the radius of gyration.

* = V^ (d! + <^)

for a hollow circular rod and

' = VA

1 BH« - bh^

12 BH - bh

for an H section rod, and /, is the two-thirds of the com-
pressive strength of the material divided by the factor of safety
allowed.

(b) The dimensions necessary to resist failure due to the axial
load and the transverse bending load require two operations to
be performed.

For the former, Gordon's formula may be applied.

P' y c

A' 1 + a^

F' is the load upon the piston when the crank is at right angles
to the connecting rod, and is the pressure (Pa — 14'7) of Art. 60,
A' is cross-sectional area of the rod at the point in the length of
the rod of maximum bending moment due to the transverse
acceleration, /« is the permissible stress, and the other symbols
have their previous significance.

For the latter, the transverse inertia force, the rod is assumed

PISTONS, GUDGEONS AND CONNECTING EODS 167

to be of uniform aeotion throughout, as the error involved by so
doing is extremely small.

Referring to Fig. 21, When the crank is nearly at right angles
to the connecting rod, the acceleration at right angles to the rod
increases uniformly from zero at C to o>V at X, so that the
diagram representing the acceleration is as shown by the triangle
CXY in the figure where XY = (M?r (<*> is the angular velocity
of the crank in radians per second, and r is the radius in feet).

Fig. 21. — Load on Connecting Rod.

At any point distant 1 from the gudgeon pin the acceleration

will be w*r j-: If w is the weight of unit length of the rod, the

inertia force upon the rod at any point distant 1 from the gudgeon

pin will be - wV t=^, and the total inertia force upon that length

w 1"

of the rod is — X «*r X ^t"- The total inertia force on the whole

g 2L

length of rod is o~^^» ^^^ ^^^ resultant will act at the

mass centre of the triangle CXY, since the diagram of accelera-
tion is a diagram of force to a different scale, that is, at a distance

-3- from the gudgeon pin. The resultant of total force in the

length 1 will similarly act at a distance g- from the gudgeon pin.

168 MOTOR CAR ENGINEERING

The reaction at the gudgeon pin end due to the total inertia

force in the rod is —p: — X -^ and for the total inertia force on

2g 8

the length 1 = — ^-^= — X -5- at the crankpin end.

The bending moment at any point distant 1 from the gudgeon
pin will be —

M = -

w(i)V

6g 6gh

(Ln - 18).

The bending moment on the rod is a maximum when M is a
maximum, but the expression outside the brackets is a constant,
therefore it is only necessary to find when (L*l— 1®) is a maximum,

and this occurs when ^^a = ®'

Diflferentiating L* — 31" =

L
1 = Vs

= 0-5773L,

that is, the point of maximum bending moment is at a distance

0'5778L from the gudgeon pin.

Substituting this value of 1 in the expression for the bending
moment,

M = -|^ { (L» X 0-6773L) - (0-6773L/ j
= 0-002 wcA-L^.

Since / = 2"

._ -0 02 wcah-L^

•^- Z

Now there are two equations to be satisfied from the above

(«)/. = Ki±^

(6)/c=/c'+/

j_ P' (1 + a p) . 0-002 tt'wVL*

A' ^

of which the only anknown quantities are w, f„ A and Z.

PISTONS, GUDGEONS AND CONNECTING RODS 169

But w = cross-sectional area of rod X weight per unit volume,
and therefore only f^, A and Z are unknown, fc is two-thirds of
the ultimate strength of the material divided by the factor of
safety. The factor of safety for this case should not be less than
8 and preferably 10, since the load fluctuates between a maximum
on ignition and zero, at slow speeds ; or between a maximum in
one direction on ignition and a maximum in the opposite direc-
tion at the end of the exhaust stroke at high speeds and is
suddenly applied — for the latter condition inertia forces in the
line of stroke have to be considered and the pressure on ignition
will be reduced considerably.

Now, assume a section for the rod, substitute the values of A
and Z in the equations and find the stress.

With a little experience and a judicious adjustment of the
assumed dimensions it is generally possible to determine the
section required on working through the equation a second time.
Further, the dimensions which satisfy (b) will usually be found
to be ample for (a). In the case of circular rods no further
calculation is required for this part, but when rods are of H
section they should be checked for strength, at ignition, in a
direction at right angles to the plane of rotation. The value of

a in Gordon's formula is then ^ttfj^ and k is V stt -rvrf rr •

oo,UUU Itfi x>xl — Oft

Having obtained the section at a point 0*5773L from the
gudgeon pin, the suction at the small end to give the required
area can now be determined, due regard being paid to considera-
tions of manufacture ; and the section at the crank pin end may
be found by setting out the rod on paper and drawing lines through
corresponding points on the two sections.

The Attachment to Crank. — The connecting rod is attached
to the crank by means of two or four bolts which secure a cap in
position. Two bolts are used where long bearings are employed
to obtain rigidity and to make the bearing more compact, but it
is probable that the weight of the part is increased slightly.
The bearing is lined with either bronze or white metal carried in
gunmetal shells, or with the white metal run into the connecting
rod end itself, but with the improved methods employed in cast-
ing white metal — the Eatonia process or die casting — it is quite
satisfactory to cast the bushes of white metal alone, thereby dis-
pensing with the weight and space required for a shell, where a

ITO MOTOR CAR ENGINEERING

shell is used, or loose lining, it should be pinned to prevent any
movement.

The bearing area is product of the length and the diameter of
the crankpin, and one should preferably not be less than |d.
The diameter of the pin is determined largely from strength con-
siderations and the length is dependent upon the pitch of the
cylinders, etc., but it is necessary to see that sufficient bearing
surface is provided. In many cases the area will be found to be
adequate, but often it is not, and since it is undesirable to
increase the pitch of the cylinders, the diameter of the crank-
shaft must be enlarged. Of late there has been a tendency to
increase the diameter of the pin to give greater tensional rigidity
to the shaft, but it has also a beneficial effect in reducing the
bearing pressures and lengthening the life of the bearing. It
should be observed, however, that the diameter of the bearing
must not be enlarged in order that the length may decrease, for
an increase in diameter should be accompained by a decrease in
the pressure, because the rubbing speed at the bearing has been
increased. Further, the frictional losses at a large diameter bear-
ing are greater than those at a smaller bearing if the intensity
of pressure is the same in both cases.

The intensity of pressure at the bearing varies between 750
and 1,600 lbs. per sq. in. (0*527 to 1*05 kilos per mm.*)— the higher
limit being used on some forced lubrication engines — but it is well
not to exceed 1,200 lbs. per sq. in. (0*844 kilo per mm.*) in the
fast-running engines that are now fitted if they are required to
run for prolonged periods. Similarly, it is preferable for the lower
limit of pressure to be not more than 600 lbs. per sq. in. (0*422
kilo per mm.*) for the best results unless the continuous supply
of lubricant is ensured at all times as, for example, when the
engine is inclined as in hill-climbing. The . load is taken to be
the pressure in the cylinder at ignition without any reduction on
account of inertia forces.

The connecting rod bolts are subject to the greatest stress when
the engine is running at high speed on the exhaust stroke and
the crank has nearly reached the dead centre. The load is an
inertia load, due to the mass of the reciprocating parts, and is

equal to Total Load on bolts = MwV f 1 + - ) • Where n is the

ratio of the connecting rod length to the crank radius, M is the

PISTONS, GUDGEONS AND CONNECTING EODS 171

mass of the reciprocating parts, o) is the angular velocity in radians
per second and r is the crank radios in feet this is divided between
the number of bolts, so that the area required for each bolt at the
bottom of the threcid is —

Area per bolt at bottom of thread = Ma)*r -^j^^: — where N is

the number of bolts and /is the permissible stress. The factor of
safety should not be less than 8, and preferably 10, since with
the small bolts used the ultimate tensile strength of the core is
not so high as that of the bar from which they are made.

The bolts should be turned down for a portion of their length
to a diameter slightly less than the diameter at the bottom of the
thread so as to increase their capacity for absorbing shook. They
should also be placed as close together as possible in order to
reduce the weight and size]of the*part.

CHAPTER IX

CRANESHAFTB AND FLY-WHEELS

103. Material for Crankshafts. — The essential qualities that are
necessary for the material used in the manufacture of crank-
shafts are strength, elasticity and hardness. The two former are
obvious from the nature and the character of the loads to which
the shaft is subjected — alternating and suddenly applied — while
hardness is needful because surfaces of softer grades of steel
seldom obtain those smooth, hard, wear-resisting surfaces that
are soon acquired by the harder grades of metal if originally in a
good condition. There are many kinds of steel that fulfil these
requirements, and the selection of any particular variety must
depend upon the designer, who will have regard to the class of
work upon which the engine is to be engaged — a reference to
Tables 7» 8, and 9 should be of assistance here.

Crankshafts are now seldom built up, but are forged from the
billet, generally drop forged, because this assists greatly in
reducing the cost of manufacture.

104. Arrangement. — With regard to the number of bearings, it
cannot be too strongly emphasised that adequate support must be
given to the crankshaft, and further, that any construction which
will reduce flexure is desirable. On account of this, the provision
of bearings between each crank although not absolutely necessary
for successful operation, is to be commended, while in addition
wear at the edges of the bearings, due to excessive flexure of the
shaft, and vibration attributable to the same cause, are considerably
minimised, and the loads upon the parts reduced.

This flexure of the shaft results from (a) the load from the
explosion and (b) the centrifugal force, acting at the cranks set
up by the revolving mass of the crankarm, crankpin and con-
necting rod end. The former may be generally disregarded in
this connection, but not so the latter. It will be found on refer-
ence to Chapter X. that a four-cylinder crankshaft is in perfect
rotating balance as a system, but if one crank alone is. considered,

CRANKSHAFTS AND FLY-WHEELS 178

the force at that crank tends to displace the bearings on either
side of it and is restrained by those bearings. If, however, there
are two cranks between two adjacent bearings, the forces are
opposed but institute a couple upon the shaft causing one crank
to deflect outwards in one direction and the other crank to deflect
in an opposite direction. At low speeds of rotation the magnitude
of the deflection is negligible and hardly apparent, but as the
speed increases the defect becomes more and more pronounced,
and disturbs the smooth running of the engine. To overcome
this effect in some engines, the crankwebs have been extended on
the opposite side to the crank so that they act more or less as
balance weights for that crank — ^it is for partially balancing each
individual crank since the shaft is balanced as a whole. It will
be readily apparent that the greater the distance between the
cranks, the greater the magnitude of flexure since the deflection
varies as the (span)^ ; that is, if the pitch of the bearings is halved,
the deflection is reduced to one-eighth of its original value. It is
not, however, always possible to arrange for a bearing between
each crank, as in en-bloc castings, except when the water spaces
between adjacent cylinders is made of large dimensions. When
there are two cranks between two adjacent bearings the con-
necting web between the crankpins is sometimes made parallel
to the outside webs (see Fig. 9), and sometimes inclined to them
(see Figs. 9 and 10, Vol. I.) The latter is more expensive to
machine, and is usually found in engines in which ample water
spaces are provided, but the construction seen in Fig. 9, Vol. II.,
shows how the use of an angled web may be avoided by swelling
up the crankpin at one end.

The arrangement of cranks has been discussed in Vol. I.,
Arts. 19—21, and the reader will probably be familiar with those
generally employed, so little need be said under this heading
here. The number of cranks is dependent upon the number and
arrangement of cylinders. In some cases, as with horizontal
engines with opposed cylinders and also in eight-cylinder vee and
in radial engines, it is possible to arrange for two or more pistons
to be operated from one crankpin, but in all cases the determining
factors are uniformity of torque and a good balance, as an engine
which is unsatisfactory in either of these respects is not likely to
attain any degree of commercial success. For car work, the one,
two, four or six-cylinder vertical engine are used by the vast

174 MOTOR CAR ENGINEERING

majority of makers, and these have one connecting rod to each
crank, although there are a few cars fitted with vee engines,
haying two, six, or eight cylinders with two connecting rods to
each crank.

Hollow crankshafts are frequently employed because for any
given weight of metal they are better able to resist the bending
and torsional stresses, they are less liable to fracture, they reduce
the bearing pressures, and the hole through the centre serves as an
oil duct for a force lubrication system. It is, however, unwise to
make the hole too large in relation to the external diameter, since
there is a risk of distortion at the journals — a ratio of external
diameter should not be greater than 0*65.

The crankpins and journals must join up to the webs in well-
rounded curves of at least ^ in. (3 mm.) radius, as parts which have
abrupt changes of form are Uable to fracture on account of the
uneven distribution of stress. The webs should be about ^ in. (6
mm.) greater in depth than the diameter of the journal, and means
should be provided to retain the shaft in a definite axial position
under all conditions of service, such as by slightly enlarging one
of the crankwebs at the journal so that it may act as a thrust
collar when declutching.

When the crankshaft is drilled for the purpose of lubrication
care should be taken that the holes do not come too near to the
junction between the web and the journal or pins (it is much pre-
ferred for the holes to be arranged as shown in Fig. 9) ; and since
the hole must be plugged with screwed plugs at the ends the
number of holes should be limited, and these carried only as far
as is necessary to give a clear passageway for the oil.

Oil-throwers, for preventing the oil from travelling along the
shaft at the rear end and giving a dirty appearance to the engine,
may be provided either by cutting a vee groove round an enlarged
portion of the shaft, or by forming a ring upon the surface of the
shaft immediately after the end-bearing and within the crankcaae
(see Fig. 4). At the front end of the shaft the timing pinion will
be fitted as well as the dogs for starting up the engine. Two
arrangements are shown in Figs. 4 and 9.

The construction adopted at the rear end of the shaft will
depend largely upon the method of attachment of fly-wheel and
the form of clutch employed. These receive attention later.

106. Ctoneral Design of Crankshafts. — Crankshafts are subjected

CRANKSHAFTS AND FLY-WHEELS

175

^ A

Fig. 22.— Stress Dia-
gram for Shafts
under Torsional
Stress.

in working to both bending and tension — bending due to the load
upon the piston and torsion from the torque transmitted — so
that before the methods of design are proceeded with it would be
well to examine the conditions which exist in a shaft subject to
such straining actions, in order that the basis upon which various
formulae used by engineers in the design
of crankshafts are founded may be better
understood.

When a shaft is loaded by a single load
the fibres are stretched on one side of the
beam and compressed on the opposite side,
inducing tensile and compressive stresses
(normal stresses) in the material on either
side of the neutral axis. Li addition there
are shear stresses induced in the material
in a plane at right angles to the neutral
axis but which are zero at the point of
appUcation of the load, that is, where the tensile and com-
pressive stresses are a maximum, so need not be considered.
Also in a shaft subject to pure torsion, the principal stress is a

shear stress, as may be seen by considering a
small square lamina on the surface of a shaft,
the sides being respectively parallel to and at
right angles to the axis of the shaft, as shown
in Fig. 22. The shear stress/, along DA, BO
produces a couple tending to displace the
lamina, and therefore, to maintain equi-
librium there must be an equal and opposite
shear stress along the sides BA and DC.
Resolving the forces which induce the
stresses along the diagonals AC, BD, it will
be seen that a tensile stress is produced on

Fig. 23.— Stress Dia- ^^ *^^ * compressive stress on BD. Thus,
gram for Shafts there is a tensile stress and a compressive
Str^^' Combined gtregs on two planes at right angles to one

another and inclined at an angle of 45

degrees with the axis of the shaft.

For combined bending and twisting, take a triangular lamina

XYZ, as shown in Fig. 2S, the stresses are the shear stress /, on

XY and YZ, the tensile stress /< on XY, the resultant shear

176 MOTOR CAR ENGINEERING

stress /«' on XZ and the resultant normal stresses//,//' on ZX
and a plane at right angles to it.

The resultant normal tensile stress on XZ

The maximum normal compressive stress on the plane
perpendicular to XZ may also be found to be

fi"=^4- JfVTiA.

and the maximum shearing stress is similarly

// = VfT+TA-

106. Formula used for Shafts subject to combined Stress. — There
are several formulae used in the design of crankshafts but the
following are those best known

Rankine (a) B, = JB + j VB* + l"
(fr) T, = B + VB^ + 'p

French B. = | B + | V B' + T«
Grfest B, = VB* + T

St. Venant B, = ? B + ^ ^B* + T«,

where Be = the equivalent bending moment, T^ = the equivalent
twisting moment, B = the actual bending moment, T = the

actual twisting moment, and ~ is Poisson's ratio.

These formulse, notwithstanding the variation in the magnitude
of the equivalent bending moment obtained from them, have all
a rational origin, and are based on the theory that failure results
from either the normal stress, or the shear stress, or th& strain
produced by the combined stresses.

The Rankine formulae are perhaps the oldest and those which
have been most extensively employed in this country. They are
founded on the assumption that the normal stress

= § + v/i + i/J

produces fracture. The Guest formulae is of more recent intro-
duction and is confirmed by the results of a number of experi-
ments carried out by him at Montreal, which indicated that the
resultant shear stress

CRANKSHAFTS AND FLY-WHEELS 177

• // = V>7 + J/?
caused the faUare of the material. This formula is not, however,
accepted in its entirety, as subsequent experiments by independent
investigators show that it is only applicable to shafts made from
soft, ductile material, and it has been suggested ^ that a variable
might be prefixed to the expression so that the formula becomes

where k for mild carbon steel is 0*77. Without enlarging further
upon the matter, as the subject is a very wide one, and a large
number of papers have been contributed to the various institutions
and to the engineering press, it may be stated that the brittle
materials fail according to Bankine's theory and ductile or elastic
materials according to Guest's.

The French or Grashof and the St. Venant formulaB are
similar in character, the latter being the general and the former

the particular form when - = 0*26. In these failure is assumed

to be caused by the strain produced by the resultant normal stress.

When - = 0-8,

B, = 0-85 B« + 0-65 VB^ + T\

For the methods by which the magnitude of the maximum
stresses are obtained, and the formulas for the equivalent bending
moment derived, the reader is referred, to textbooks on the
strength of materials.^

In applying these formulae for any given stress and bending and
twisting moments it will be found that, excepting the Guest's
formula, there is little variation in the dimensions obtained, partly
owing to the comparatively small value of the moments acting,
partly because the resistance of the shaft to fracture varies as the
cube of the dimensions, and partly because the formulae differ
little in themselves. The dimensions will be smallest in Bankine's,
the French next, St. Yenant's next, and largest with Guest's.

The Author has found the formula quoted above, where - = 0'3,

to give very satisfactory results in practice, and this will be used
throughout the book.

1 See Engineerinf).

« See Morley'B " Strength of Materials."

M.C.E. N

178 MOTOR CAR ENGINEERING

107. The Design of the Crankshaft. — For the purposes of design,
crankshafts mast be divided into classes according to the number
of cranks between adjacent bearings. Thus, a three-bearing shaft
for a two-cylinder engine, a five-bearing for a four-cylinder
engine, and a seven-bearing shaft for a six-cylinder engine are
all in the same class, and shafts with two cranks between two
adjacent bearings are in another class. The former will be
designated Glass I. and the latter Class II.

It is first necessary to obtain the positions at which the
maximum straining actions occur, and these may be determined
either by drawing an equivalent bending moment diagram for
the bending and twisting moments on the shaft or by estimation
of the magnitude of the acting moments. The latter is to be pre-
ferred, since it is known that the maximum bending moment on
the shaft occurs when one crank is on the top centre at the point
of ignition, while the combined bending and twisting moments
produce the maximum straining action when the crank is at
about an angle of 40 degrees with the line of stroke from the
inner dead centre. These positions may be verified graphically,
but will be found to be approximately correct with a ratio of the
connecting rod to crank of 4*25 to 1. The former method is more
exact, but a considerable amount of labour is involved, especially
as the diagram must be constructed for two or nore points along
the shaft in a multi-crank engine with a Glass II. shaft, while the
error involved in the Jatter method is negligible for all practical
purposes.^ The equivalent bending moment diagram is drawn
from calculated values of the twisting moment on the shaft for
various crank positions (these may be taken from a twisting
moment diagram, uncorrected for inertia), and the bending
moments on the shaft due to the loads upon the pins at the posi-

.. -J J / twisting moment \ i_. i_ . . ,

tions considered ( = ; — ^— -p -, ^. — which are inserted

\ equivalent crank radius/

in the formula for equivalent bending moment and the results
plotted. If desired, only a portion of the diagram may be drawn
for the crank angles in the vicinity of 40 degrees from the line of
stroke. The inertia of the reciprocating parts is neglected because
the maximum straining actions occur at starting, and when run-
ning at low speeds with full throttle. In some cases designers find

1 Headers who desire to see the method i^f working; employed may refer to the
Transaetiafu oft/ie Inttitution of Naval ArehitecU^ Vol. XLIV.

CRANKSHAFTS AND FLY-WHEELS 179

the maximam twisting momenli upon the shaft from the mean

twisting moment by multiplying by the ratio twisting

moment. The mean twisting moment in lbs. inches is obtained
from

^ _ HP X 88,000 X 12

-imean - 27rN

where r is crank radias in inches, and N is the number of revo-
lutions per minute at which the stated horse-power is developed.

The ratios of twisting moment for several engines are

mean ^ ®

given on p. 196, where the value of the inertia force at the

inner dead centre has been taken as equal to 100 lbs. per square

inch (0*0708 kilo per mm.^), and the compression pressure ais

75 lbs. per square inch (0*0527 kilo per mm.*).

Considering the crankshafts in the two positions indicated,
namely, with the crank on the inner dead centre, and at an angle
of 40 degrees with the line of stroke, the cylinder operations are
as shown in tabular form on p. 180.

For the purpose now being considered the cylinders marked
with an asterisk may be entirely neglected, since the pressure act-
ing on the piston is of such small value in the positions examined.
It will be seen that, excepting in the six-cylinder engine, the
maximum straining actions are due to one cylinder only. The
table may be compiled for other cranks if desired, with the proviso
that in the case of a six-cylinder engine, the firing crank should
be after the other cylinder on the power stroke for the bending
moment data and that the power crank is before the crank on
the compression stroke for the equivalent bending moment data.
These will then always represent the maximum straining
positions.

The design of the crankshaft is in four parts, (a) the crankpin,
(b) the crank webs, (c) the journals, and (d) the couplings.

108. The Crankpin. — The crankpin is subjected to combined
bending and twisting, the bending moment due to the load upon
the piston and the twisting moment from the torque transmitted.
In determining the bending moment on the pin, it will be assumed
that flexure takes place from the centres of the bearings. This
assumption is necessary because in design the maximum strain-
ing action must be considered, and with the main bearings

N 2

180

MOTOR CAR ENGINEERING

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CRAKKSflAFTS AND J^Lt-WflEELS

181

ordinarily used there is little doubt that they t^ist sufficiently to
allow this to take^ place. If this were not so, there would be a
high intensity of pressure at the edge of the bearing, probably
sufficient to cause metallic contact and abrasion, but it is well
known that the edges of bearings are seldom more subject to wear
than are the other parts of the bearing. Where four bolts are
employed in combination with a long bearing, rigidly constructed
and well webbed, it may be safe to treat the shaft as a beam with
fixed ends or as supported at the inner edges of the bearings, but
not otherwise. It is not considered that the shaft can be regarded

Fig. 24.— Crankshafts.

as a continuous beam in any case because of the irregular load-
ing. At the position of maximum bending moment for Glass I.
shafts, the reactions at the centres of the bearings are each B.
Let L be the pitch of the bearings. Then the bending moment

at the centre of the pin will be -^=--j-, where P is the total

load upon the piston.

For Class 11. shafts, if 1 is the distance between the centres of
the cranks (Fig. 24), the reaction at the bearing nearest the firing

crank will be ^j — ■ and at the other bearing ^ ^, so that

the bending moment at the centre of the pin of the firing crank

182 MOTOR CAR ENGINEERING

But in both classes of shafts for six-cylinder engines No. 6 crank

is transmitting the torque from No. 2 cylinder, so that if Pi is the

pressure on the piston and n the equivalent crank radius, the

torque on the shaft is Pi?!. In the case of a Glass I. shaft this is

transmitted through the crankpin of No. 6 crank and is the

twisting moment that has to be added to the bending moment

above ; but in the case of a Class 11. shaft this torque Fin is

equivalent to a force F at the crankpin of No. 5 crank which acts

through the centre crank web and produces a torque F X 2r,

Piri

where r is the radius of the crank. But F = , and therefore

the twisting moment on the pin of No, 6 crank is — ;— X 2r

= 2Pi?'i. It should be noticed that the centre web doubles the
twisting moment on the pin.

For the maximum equivalent bending and twisting moment in
Class I. shafts from the table there is no twisting moment on the pin
of No. 1 crank ; there is a twisting moment on all the other cranks
and a twisting moment and a bending moment on No. 4 crank of
a six- cylinder engine. The bending moment on No. 1 crank will
obviously be less than that at ignition, since there is then a
greater load on the pin, and may therefore be neglected, as may
also be the equivalent bending moment to the twisting moment
on the other cranks excepting that at No. 4 crank of a six-
cylinder engine. With a pressure in No. 4 cylinder of a six-
cylinder engine. No. 8 of a four-cylinder engine, and No. 2 of a two-
cylinder (180°) engine of Pa, the reactions at the bearings are Pa

and the bending moment -^-. The twisting moment is Pgia,

where P2 is the pressure in No. 1 cylinder and rg is the equivalent
crank radius. Combining these moments by means of the
formula, the equivalent bending moment may be obtained.

For a Class II. shaft the bending moment from No. 1 crank
will be transmitted through No. 2 crank, con equently No. 2 crank
will be subjected to both bending and twisting, which will be at a
maximum near its junction with the centre web. The twisting
moment will be 2P2/2, being doubled by transmission through the
centre crank web.

The reactions at the front and rear bearings are ^ ^J* and

CBANKSHAFTS AND FLY-WHEELS

183

Pa (L ^ 1)
2L

respectively, and the bending moment at the junction

of No. 2 pin with the centre web will be

P2(L-l)^L-l + li

2L 2

where li is the length of the crankpin. By substituting these
moments in the formula for the equivalent bending moment, and
equating to the moment of resistance of the shaft, the diameter
may be obtained. The bending moment at No. 4 crank for six-
cylinder engines and No. 8 crank for four-cylinder engines has been
neglected in this class of shafts because the straining actions are
of smaller magnitude at that crank than at Nos. 1 and 2 cranks.

The following data are employed to illustrate the method of
working for an engine with cylinders of 100 mm. bore and having
a stroke of 150 mm.

Class I. Shaft.

CLiSi II. Shaft.

L
1

150 mm.

55 mm.

266 mm.

106 mm.

55 inm.

In an engine using a compression pressure of 0*056 kilo per
mm.*, the explosion pressure will be 0*225 kilo mm.* (see Art. 60),
and if the ratio of connecting rod to crank is 4*25 to 1 —

Pressure.

liOad on Piston.

P at ignition ....
Pi at 60° before bottom centre
Pa at 40° after top centre
Ps at 80° before top centre
ri at 60° before bottom centre
ra at 40° after top centre
Vs at 80° before top centre

0*225 kilo mm.*
0-086 kilo mm.*
0-105 kilo mm.*
0*14 kilo mm.*

57-0 mm.

76*0 mm.

1,767 kilos.
283 kilos.
825 kilos.
110 kilos.

Considering the cranks in the position of maximum bending
moment, the reactions are 888*5 in Glass I. shafts and in Glass IL
shafts 581*5 and 1,285*5 at the front and rear bearings of a six-
cylinder engine and at the rear and front bearings in two and four-

184 MOTOR CAR ENGINEERING

cylinder engines. The bending moment at the centre of No. 1
crank of two and four and at No. 6 crank of six-cylinder engines is for
Class I. 833-5 X 75 = 62,500 kilos mm. and in Class II. 1^285-5
X 80 = 99,000 kilos mm. At No. 6 crank of a six-cylinder engine
there is also the twisting moment 288 X 57 = 16,100 kilos mm.
for Class I. and 288 X 57 X 2 = 32,200 kilos mm. for Class II.

Then for Class I. shafts for two and four-cylinder engines —
Bending moment = 62,500 kilos mm.

For Class I. shafts of six-cylinder engines —

B, = 0-35 X 62,500 + 0*65 ^62,500^ + 16,100^

= 68,800 kilos mm.
For Class II. shafts for two and four-cylinder engines —

Bending moment = 99,000 kilos mm.
For Class II. shafts for six-cylinder engines —

B, = 0-35 X 99,000 + 0-65 ^99,000^ + 82,200^

= 101,800 kilos mm.
The same reasoning may be applied to Nos. 4 and 1 cranks of
a six-cylinder engine or to any other pair of cranks where the
crank considered on top centre is after the crank on the power
stroke and next to the rear bearing in a Class II. shaft.

For the position of maximum continued bending and twisting
moment.
The bending moment for a Class I. shaft is —

PaL _ 110 X 150 ..om-i

-^ =z = 4 120 kilos mm.

4 4

The twisting moment is Para = 825 X 57

= 47,000 kilos mm.
The bending moment for a Class II. shaft is —

PajCL - 1) L - 1 -fli _ 825 (266 - 106)
2L 2 2 X 266

266^ 106 + 55 ^ 26,600 kilos mm.

The twisting moment is 2Para = 2 X 825 X 57

= 94,000 kilos mm.
Be for a Class I. shaft —

B, = 0-85 X 4,120 + 0-65 ^4,120* + 47,000^

= 82,040 kilos mm.

Be for a Class II. shaft —

B, = 0-35 X 26,600 + 0*65 ^26,600^ + 94,000^

= 107,300 kilos mm.

CRANKSHAFTS AND FLY-WHEELS 185

Thus, for the particular dimensions assumed, Glass I. shafts are
to be designed for the maximum bending moment and Glass II.
shafts for a maximum equivalent bending moment to the com-
bined bending and twisting.

This, in general, will be so, but is not always the case, since it
depends upon the length of stroke and the pitch of the bearings,
and, therefore, it is desirable to examine the conditions for every
design.

The diameter of the pins (which will be made the same
throughout) may be found by equating the equivalent bending
moment to the moment of resistance of the shaft.

Thus, if steel of 100 kilos per mm.^ (68*5 tons per square
inch) is used the permissible stress will be from 10 to 12*5 kilos
per mm.^, since the factor of safety should not be less than 8 and
preferably 10.

It may be observed that the actual factor of safety is in excess
of that indicated, since the piston friction will reduce the load by
some 10 per cent., and in determining the actual factor of safety
regard should be paid to the class of steel — with steel having an
elastic limit high compared with the ultimate tensile strength
and a good elongation the lower factor can be quite safely used.
The stress used may be with advantage reduced in six-cylinder
shafts 80 as to avoid the effects produced by torsional oscillations.

Then taking a Glass I. shaft of a four-cylinder engine with the
above data —

d = 40 mm.
For Glass II. shaft

107,800 = ^d«/ = ^rPx 10

e{ = 48 mm.

Now check for bearing pressure. The pressure at ignition is
1,757 kilos, and it was assumed that the length of the pin was
55 mm., so that the bearing areas will be 2,200 mm.^ and 2,640
mm.' for Glasses I. and II. shafts respectively. Hence, the
intensity of bearing pressure will be 0*8 kilo and 0*66 kilo per
mm.' for the two classes — the limits of pressure given in Art. 102,
p. 170, being 0*527 to 1*05 kilos per mm.'

Note. — The length of the crankpin will not be determined in

186 MOTOR CAR ENGINEERING

the arbitrary manner above indicated, but will be chosen so that
in conjunction with the diameter it provides sufficient bearing
area and at the same time can be conveniently arranged for in
the length available, the latter being largely determined by the
pitch of the cylinders and the number of bearings. A length
will, however, have to be assumed in the first instance and
adjusted later. It is desirable to limit the diameter, since by so
doing the size of the connecting rod end is reduced ; although,
as the length of the pin decreases, the overall length of the engine
within certain limits may also be decreased.

109. The Crankwebs. — The straining actions on the crankwebs
are not only complex but also in a large measure indeterminate,
since the manner in which the shaft distorts is somewhat obscure,
and therefore the principal straining actions only will be
considered.

In a Class I. shaft at ignition there is a normal compressive
load which is distributed between the two webs and a bending
stress at right angles thereto. If the load on the piston is W,
the webs are b wide along the shaft, h deep, and x is the distance
between the centre of the web and the centre line of the bearing.

Then the normal stress is the load divided by twice the sec-

W W

tional area of- webs = ^rr* The reaction at the bearings is -^

Yfx

and the bending moment on the web -^,

and^ = iftfeV
2 6 '

^'- Tip-
so that the total stress = •rrr + -rro--

If the shaft is transmitting torque from another, as it will be
if there are more than four cylinders, there is also a torsional
stress in the web, albeit this will be small in a six-cylinder engine.

When the crank has turned through an angle of 40 degrees
from the iniler dead centre there is —

(a) A bending moment on the web due to the torque trans-

mitted ;

(b) A normal stress in the web due to the resolved part of the

CRANKSHAFTS AND FLY-WHEELS 187

force acting at the crankpin in the direction from the
pin to the axis of the shaft ;
(c) A torsional stress in the web due to the force at the pin
acting at a distance from the axis of the web.

Let Pa be pressure at 40 degrees past top centre, r the radius of
crank, d the diameter of the shaft, and y the distance between
the centre line of the cylinder and the centre of the web. The
angle between the connecting rod and the tangent to the crank
circle is 0, and the resolved part along the crank is Pa sin 0, and
the component tangential to the crank circle (the effective
pressure for torque at radius r) is Pa cos 0.

Then the bending load at the part of the web near the journal

is Pa cos ir — ^ j

F'eo&e (^-2) "^l^^^f

r_ 8P' COB (2r — d)

^ hi? •

The normal stress is — ^, — ,

since the resolved part of the load upon the rod is distributed
equally between the two webs.
The torque is Pa2^.

y _ Pay (Sfe -f l'8fc)

This bending and the torsional stress will be augmented if the
crank is transmitting torque from another cylinder.

It is clear that the exact determination of the stresses is not
easy, especially as the standard formulae for combined stresses
are applicable only to circular shafts, and therefore the web is
designed for the position at ignition and then checked to see that
the value of the bending and normal stresses at 40 degrees past
top centre does not exceed 80 per cent, of the permissible stress,
the other 20 per cent, being an allowance made for the torsional
stress, which is otherwise neglected.

> This formula for the torsional resistance of a rectangular shaft is taken from
Morley's *' Strength of Materials."

188 MOTOR CAR ENGINEERING

Thus, with the data previously employed and the added
assumption that x is 87 mm. and that b = Oih (say) : —

m . 1 t ^ • '^' 1»767 _L 8 X 1,767 X 87
Total stress at ignition = ^,. H tt^

f _ 1,767 196,187

•^ " 0-8A« 0-16/i« • .

/should not exceed 10 kilos per mm.'
Hence,

8ft8 - l,767fe - 980,686 = 0.

h = 50 mm.
6 = 20 mm.
Checking as stated above for the second position, after noting
whether the assumed distance x is subject to any appreciable
error, — Pg = 826 kilos, the value of for a connecting rod of
4'25 cranks is 41^ degrees, and taking the diameter of the shaft
to be the same as that of the pin,

Total stress - « X 825 cos 41^ (2 X 76 -'40) 826 sin 41^
lotal stress - 80 X 20« + 2 X 20 X 60

= 4*26 kilos, little more than one half of the per-
missible stress.

It will be observed that the value of ft = 60 mm. will
permit of a good radius at the junction of the pin with the
web.

For Class II. Crankshafts the procedure for the outer webs is
similar to that outlined above, but it should be observed that the
load on the piston is not equally distributed between the two
webs, since they are at unequal distances from the point of
application of the load. It is also desirable to use a slightly
lower stress in the case of a six-cylinder shaft to allow for the
torque on the web from, say. No. 8 cylinder if No. 6 is considered,
or No. 2 cylinder if No. 6 is considered, or No. 1 if No. 4 is
considered. It will be found that the dimensions of the webs are
66 mm. by 21 mm.

The centre web is, however, subject to peculiar twisting and
bending actions. When Nos. 8 and 4 cranks are transmitting
power from Nos. 1 and 2 the torque causes an angular strain of
the shaft, the front web twists relative to the rear web and
carries with it the crankpins and centre crank web, thus induc-
ing a torsional stress in the latter and a bending stress in the
former. It will also induce a. bending stress in the journal the

CRANKSHAFTS AND FLY-WHEELS 189

magnitude of which it is impossihle to estimate. At the same
instant the force acting at the end of the centre web near its
junction with No. 8 crank is of magnitude T such that Tr is the
torque, but in transmitting this to No. 4 crank this force T acts
through a length 2r, so that the torque on No. 4 pin is 2Tr (as
stated previously on p. 182). This causes a bending moment
on the web near its junction with No. 4 crank and represents,
with the twisting moment ahready on the web, the severest condi-
tions of service. Those conditions, so far as they relate to the
centre web, also apply when No. 8 crank is producing the torque
upon the shaft, except that the twisting moment on the web is
not quite so great, because the force on the piston is applied at
the centre of the pin, although it may be augmented in the case
of a six-cylinder shaft at No. 5 crank by the torque from No. 8
crank.

The torsional stress is allowed for by designing only for the
bending moment and using a stress 80 per cent, lower than that
in the pin.

Thus, for the shaft considered previously, the torque is 825 x

68, equivalent to a force at the crankpin of =^ — kilos. So

that the bending moment on the web near its junction with No. 4

pin is =^ (150 — 24) kilos mm.

825X68 ^ J5Q - 24) = 1 bh%

But h will be the same as for the outer webs, 55 mm., and /^

70
should not exceed 10 X tt^ = 7 kilos per mm.^ from which, by

100

substitution,

b = 26*7 mm., say 27 mm.

This dimension is measured at right angles to the line through
the centre of the web— it will be along the axis of the shaft in
the case of a shaft with a centre web parallel to the two outer
webs.

] 10. Crank Journals. — Crank journals for car engines are most
frequently designed for bearing area alone, as with solid shafts
and the limitations imposed by the overall length of the engine,
provided that the bearing area requirements are satisfied, the
strength is usually sufficient. For this reason, and in order to

190 MOTOR CAR ENGINEERING

reduce the efifects produced by torsional oscillation, solid shafts
are commonly made with journals of the same diameter as
the pin, sometimes slightly larger. With hollow shafts, how-
ever, especially if the internal diameter is made very large in
relation to the external diameter, it is necessary to check for
strength.

The permissible bearing pressure varies between 600 and
800 lbs. per square inch (0*42 to 0*56 kilo per mm.*), the
higher limit being used on some forced lubrication engines,
although in contemporary practice slightly higher and lower
values are sometimes used. But it is undesirable to employ
excessive pressures, since engines are thereby handicapped at the
outset and are unlikely to ever gain a reputation for either
reliability or durability. The rear bearing of the engine should
certainly not be so highly loaded on account of the weight of the
fly-wheel at that end which is continually acting at the bearing,
and' this in some small measure may be said to apply to the front
bearing, since the timing gear and pumps are usually driven from
the shaft at this end. The pressure should therefore be reduced
to from 500 to 600 lbs. per square inch (0*85 to 0*42 kilo
per mm.*), and if the rubbing velocity of the journal exceeds
10 feet per second these pressures should be decreased
accordingly.

The load considered is the pressure on the piston at ignition,
which in a Glass I. crankshaft is distributed equally between the
two bearings, but in a Glass II. shaft the load on each bearing is
inversely proportional to its distance from the centre of the
connecting rod, that is the point of application of the load ; the
most highly loaded bearing is, therefore, that nearest to the firing
cylinder.

In checking the dimensions at the journals for strength with
hollow shafts, it is sufficient to consider the conditions existing
when the power crank is at an angle of 40 degrees from the inner
dead point (the rear crank of any pair will be the power crank in
a Glass 11. shaft). The crank journal is then subject to a bending
moment from the load on the crank and a twisting moment due
to the torque transmitted, the maximum straining effect being
produced near the junction of the journal with the web. Let R
be the reaction at the centre of the rear bearing (since the torque
is transmitted through this bearing) due to the load Pa on the

CRANKSHAFTS AND FLY-WHEELS 191

crank and ra be the equivalent crank radius. Then if I2 is the
distance between the centre of the rear bearing and the rear side
of the web (= half length of journal)—

Twisting moment = Para,
Bending moment = Bala-
By substituting these in the formula for the equivalent bending
moment and equating the result to the moment of resistance of

the shaft = ^ ^i — ~ff ^^® values of D and Di, the external

and internal diameters respectively may be determined. It will
facilitate the working if a ratio be assumed at first between D
and Di and then adjusted as necessary when the value of D is
ascertained.

111. The Coupling. — The coupling itself does not lend itself to
great variations in design but simply consists of a flange solid
with the shaft through which holes are drilled for the attach-
ment of the fly-wheel. The shaft should be thickened up
between the flange and the engine so as to give stiffness and
thus prevent flexure through imperfect clutch contact or other
cause. The diameter of the coupling is not important so long
as there is ample room for the boltheads to seat well, but it
will generally be found that the design of clutch adopted limits
the smallest and sometimes the largest pitch circle of the
bolts that can be conveniently employed, and consequently the
overall diameter of coupling. Care should be taken to ensure
that there is sufficient clearance for the boltheads, and that the
bolts can be readily removed without disturbing the shafts. The
thickness of the coupling should be made about one-fourth of the
diameter of the shaft.

But the construction of the end of the shaft will depend, to
some extent, upon the clutch design. With the cone clutch, with
or without central springs, it will be found desirable to extend
the shaft so that it may carry the moving member and keep
it in a central position and render the clutch self-contained. If
the multiple disc type is adopted it is possible to end the shaft
immediately after the coupling, the alignment of the clutch
being maintained by mounting the parts on a collar formed
upon the shaft or upon the fly-wheel itself or by providing a
bushed or ball-bearing in which the end of the clutch shaft may
rotate. In all cases, however, it is generally preferable to extend

192 MOTOR CAR ENGINEERING

the shaft, as it gives a more simple and less troublesome
construction.

The bolts for the purpose of attaching the fly-wheel, etc., are
designed for shear, and the factor of safety allowed is from 10 to
12. They are usually made of a lower grade of steel than that
used for the shaft.

The twisting moment on the shaft is

B.H.P. X 83,000 X 12 m • U lU rp ^ H.K l l

2^ = T mch lbs. = T X 11 5 kilos mm.

The torque at a radius r inches = - lbs. and at r mm. =

l2<Ji-« kilo«.
r

Let n = number of bolts. Then the shearing force on each

T T X 11'5

bolt = — lbs. or kilos, so that if the permissible stress

nr nr

in lbs. per square inch or kilos per mm.^ is /« the cross-
sectional area of each bolt is — 7- square inches or 7 —

nrf, ^ nrf,

mm.^, from which the diameter of the bolts may be obtained.
This diameter is the actual size of bolt and not at the root of the
thread, since the full sectional area of the bolt is subject to
shear. The value of r in either inches or millimetres is the
radius of the pitch circle of the bolts and must be such as can be
conveniently arranged for. It is hardly necessary to add that
the nuts should be well secured, and preferably castle nuts should
be employed on account of their enclosed position.

112. Torsional Bljg^dity. — In most engine problems it is cus-
tomary to assume that the crankshaft rotates at a uniform angular
velocity, but owing to the impulsive character of the load and
the elastic nature of the material between the engine and the
road wheels, the actual speed is by no means constant ; while the
elasticity of the shaft itself permits of local fluctuation in the
angular speed at the various cranks, that is, there is a varying
angular strain of the shaft.

Further, the load upon the piston causes the shaft to deflect,
so that the centre Une of the shaft no longer coincides with the
axis of rotation. There may also be a shortening up or
lengthening of the shaft when the crank webs are twisted and
the crankpin bent in transmitting torque. It will bo observed

CRANKSHAFTS AND FLY-WHEELS 193

that these strains are periodic since the forces producing them
occur at regular intervals of lime, and that they are (1) a tor-
sional strain (2) a transverse strain, and (8) a longitudinal
strain. But when an elastic material is strained in any manner
within the elastic limit and the restraining force is removed it
will perform an angular, a transverse or a longitudinal vibration
according to the manner in which it is loaded, exactly the same as a
coiled, a fiat or a helical spring, although the analogy must not
be taken beyond the motion imparted to the springs, so that it
will be immediately defiected in the opposite direction and then
back again, the oscillations continuing until damped out by the
internal or external frictional resistances. These vibrations are
termed free or natural vibrations of the shaft, and have each a
periodic time, that is, a certain time is taken to execute each
movement which for a simple straight shaft can be readily
calculated. It is known that the strain varies as the stress,
therefore if the strain is increased, the stress will be increased in
like proportion.

Now imagine that while the shaft is executing a movement
another force is impressed upon it, so that it causes a strain
in the same direction as that which is taking place due to the
natural vibration of the shaft. It will be clear that any such
force will have the effect of increasing the magnitude of the
strain of the material and, therefore, of the stress induced in it.
Such a vibration is then termed a forced vibration, and if the
new force is periodic and the times at which it is applied to the
shaft coincide with the time of vibration or with multiples
thereof, the effect will be to augment the strain and consequently
the stresses and thus necessitate the employment of stresses
below those permissible with other methods of loading.

In general, it may be said that with the speed of revolutions
now used the transverse and longitudinal strains may be
neglected in crankshafts and the torsional strain also in all
excepting six-cylinder shafts or those having a higher number of
cranks. In six-cylinder shafts, however, this condition of reso-
nance is often experienced and makes itself evident by the
excessive vibration of the engine, but may be eliminated by the
use of sufficiently low stresses in the design which will give a
larger diameter and consequently a greater moment of inertia.
The vibration and noise result in a six-cylinder engine from

M.C.E. o

194 MOTOE CAB ENGINEERING

three causes, the first being that when considering the balance
of the engine it is assumed that the cranks are disposed about
the axis of rotation in a certain manner — that they are arranged
in pairs, 1 and 6, 2 and 5 and 8 and 4 being, on the same centre,
and that there are 120 degrees between each pair of cranks — and
any deviation from such an arrangement will not form a balanced
system. Secondly, the angular velocity of all the cranks must
be the same, otherwise the centrifugal force produced by them
and their attached masses will vary. Thirdly, the distortion of
the shaft causes a variation in the timing of the valves and of
the ignition, so that this also will conduce to irregular explosions
and an unequal distribution of power.

It is not proposed to investigate the conditions which exist
in the shaft as such procedure would of necessity be of an
elaborate and complex nature ; it would also be of a very
approximate character since the straining actions on the shaft
are very involved and the results obtained would rest largely for
their correctness upon the validity of the assumptions made.
Readers are therefore referred to text-books ^ dealing with the
subject and to papers ^ read before the various institutions and
societies.

118. Fly-wheel. — Fly-wheels are made either of cast iron or cast
steel, the latter being used especially on very fast-running
engines or for fly-wheels of large diameter. They should always
be bolted and not keyed to the crankshafts to which they are
attached, because the see-saw effect referred to in Vol. I., Art. 22,
soon disturbs the fit of keys and causes a ''knock" in the
engine. The construction adopted will be to a large extent
determined by the clutch employed, that is, whether a disc or a
cone clutch. If the fly-wheel acts as a fan for drawing air
through the radiator, blades may be fitted to the periphery of
the wheel, or the wheel spokes may act as fan blades. The
latter is somewhat less costly but tends to limit the clutch
dimensions while the former restricts the outside diameter of the
fly-wheel. •

The resistance offered to the passage of the car is fairly con-
stant over a limited period, but the crank effort varies consider-

1 Morley's " Strength of Materials."

2 Transactions of Institution of Naval Architects^ Vol. XLIV. ; Proceeding*
of th€ Institution of Civil Engineers,

CRANKSHAFTS AND FLY-WHEELS 195

ably as will be seen on reference to Table XIY., so that at times
the energy is in excess of that which is required to propel the
car at the desired speed and at others it falls below it. This
variation in crank effort is due to two causes — the wide limits of
pressure in the cylinder and the variation in the effective crank
radius. The motion of any mass unacted upon by any outside
force is one of uniform velocity, but the motion of the recipro-
cating parts is subject to great changes in speed, and this is
possible, without shock, because of their small mass. The force
required to produce these changes in velocity is, however,
accounted for by correcting the indicator diagram for inertia, and
may therefore be neglected for the purposes under consideration.
The crankshaft and other rotating parts have little inertia to
resist changes in velocity and therefore it is necessary to add
some rotating body to the shaft having a large moment of
inertia that will prevent those rapid changes in velocity and the
accompanying high stresses in the mechanism in and between
the engine and the road wheels, due to the attempted rapid
acceleration and deceleration of the parts and which it is difficult
to produce without excessive wear on the tyres, etc., because of
the mass of the car itself. Hence the fly-wheel serves a double
purpose, namely, the storing up and restoring of energy as and
when required and the removal of shock, wear and high stresses
upon the engine and transmission. It may also be said to be of
service in assisting in the smooth running of the engine when
letting in the clutch, especially if this is done at all jerkily. It
will be clear that the weight of fly-wheel required for any engine
will depend upon the magnitude of the excess of energy over the
mean, and will consequently be greater for a single-cylinder
engine than for a six-cylinder engine, and it may be added that
the fly-wheel is of greatest service for eliminating shocks and
vibration at low speeds because of the assistance given by the car
itself at high speeds. It is, however, usual to design for normal
speed at full power. The table on p. 196 is therefore appended,
and in compiling same the inertia pressure on the inner dead
centre has been taken as equivalent to 100 lbs. per square inch
(0'070S kilo, per mm.^), and the compression pressure as 75 lbs.
per square inch (0'0527 kilo, per mm.^).

The overall diameter of the fly-wheel is limited only by the
space available between the side frames, but it will be generally

o 2

196

MOTOE CAR ENGINEERING

found to be desirable to allow ample clearance for taking out the
engine.

TABLE XIV.

Ratio of Maximum to Mean Crank Effort and of Excess

Energy to Mean Energy.

Number of Cylinders.

Ratio of Maximum to

Ratio of Excess Energy to Mean

Mean Crank Effort.

Energy per Revolution.

11-5

8^6

2 — 18(,°

5-8

1-4

2 - 860°

5-1

1-42

4-8

•91

2-73

•8

1-85

•19

1-58

•17

The maximum peripheral velocity with cast iron should pre-
ferably not exceed 80 ft. per second although 100 ft. per second
is sometimes used. With cast steel 120 ft. per second can be
safely employed. These are not dependent upon the section of
the rim as may be seen from the following : — •

W
The radial centrifugal force per unit length of rim is -^ «^r

where W is the weight of unit length of rim ; «, the angular

velocity per second and r, the mean radius of the rim in feet.

The resultant centrifugal force of the semicircular arc of the rim

W
is — ojV X 2r and bursting is resisted by a section 2A, so that

the stress induced is — w^r X 2r -r- 2A but W = kw where w =

the weight of a bar of the metal 1 in. square and 1 ft.

long.

An'(oh* X 2r
Hence the stress = —

u'<i>h^

^2A
lbs. per sq. in.

an expression in which the section of the rim is not considered.

CRANKSHAFTS AND FLY-WHEELS 197

From the construction commonly employed, whereby the rim
is attached to the boss by a plate web, there are no bending
stresses of any magnitude induced in the rim by the centrifugal
force and even with fly-wheels fitted with fan spokes, the latter
are usually arranged so close together (about 7 or 8 being
employed) that these stresses may be almost neglected. The
plate web should not be made unduly thin, not less than say
0"5 in. (12'5 mm.) otherwise there may be some " whip '* in
the wheel.

In calculating the proportions of the wheel it is usual to
neglect the webs, spokes, boss, shaft, etc., since they have but
small amount of inertia compared with that of the wheel itself.
The permissible fluctuation in speed varies with different designers,
so that no hard and fast rule can be given, but if it be taken as
8 per cent, at normal engine speed for four- or six-cylinder engines,
and 6 per cent, for one- or two-cylinder engines very good results
may be anticipated.

114. Determination of Size of Ply-wheel. — The energy stored up
by a fly-wheel in changing from an angular velocity of coi to wg is

where W is the total weight of metal in the rim and k is the
radius of gyration in feet. If the B.H.P. of an engine is H at N
revolutions per minute, the ratio of excess energy over mean
energy is A, \ is the fluctuation in speed per cent.

Energy to be stored up by fly-wheel = AH X 83,000. Per-
missible increase in speed is ^^ N since the fluctuation is dis-
tributed one half above and the other half below the mean speed,

^, , 27rN ,. , , 27rN /200 + A\

so that ft)i = -T^ radians per second and W2 = -npr 1 — kkk — )

radians per second.

Then, assuming a convenient radius of gyration, ha virg regard
to the type and size of clutch and the distance between the side
frames, all the quantities are known excepting W, and this may
be calculated.

Example : — Find the proportions of a fly-wheel for a four-cylinder
engine of 80 B.H.P. at 1,200 revolutions.

W„ =:

198 MOTOR CAR ENGINEERING

From Table XIV. the value of A is 0"3, hence the energy to be absorbed

. 03 X 30 X 33,000
per revolution is . <^>y^ = 247*0 ft. lbs.

(Kj = — ^^ — = 125-66 radians per second

~~ds ( — 90Q ) = 127-55 radians per second.

Assuming a radius of gyration of 8 in. = 0*667 ft.

247-5 = \ \ 3^/' (127-55'^ - 125-66'^)

W = 75-5 lbs.
The radius of gyration of a circular ring of metal of rectangular

section is V^ (D^ + d^).

Assuming that the fly-wheel ring has such a section and that d is
3 in. less than D, V^ (D2 + d^) becomes '^^{ID'^ - 6D + 9).
Therefore 8 = J (2D2 - 6D + 9)

D = 17-42 say 17*5 in.
d= 14-42 say 14-5. in.
It will be seen that the error involved by assuming that the radius of
gyration it the mean of the internal and external diameters would be

quite negligible..

The weight of the rim is to be 755 lbs. and therefore its volume

must be ^^^ cubic inches (if the Weight of a cubic inch of metal is
0-27 lb.) = 279 cubic inches.

The volume of the rim is j (17-52 __ 14.52) 5, where b is the breadth

of the rim.

Therefore J (17-52 _ 14.52) 5 = 279,

b = 3-7 in.

CHAPTER X

THE BALANCING OF ENGINES

The investigation of problems in connection with the balancing
of engines, especially of those in which the construction employed
differs from that usually met with, affords one of the most
interesting studies in engine design, and in this chapter the
general principles involved will be considered.

It should be observed, however, that in the petrol engine, the
placing of the cranks or the disposition of the cylinders is deter-
mined largely by the desire for the regularity of the impulses
given to and the uniformity of torque on the crankshaft, and this
accounts for the symmetrical arrangements which are so common.
But when these are satisfied there still remains the question of
the balance of the engine, which must receive the most careful
attention.

115. Importance of a Gtood Balance. — Too much importance
cannot be attributed, nor can too much care be bestowed on a
deaigA to ensure that the engine shall be as nearly perfect in
balance as possible, for the presence of any unbalanced part in a
high-speed engine soon becomes apparent, owing to the excessive
vibration produced thereby. This is especially so as regards the
motor-car engine, for it not only runs at high speed but it is also
mounted on an extremely sensitive framing, and the inertia forces
increase in magnitude as the square of the speed. Largely from
this cause the advent of a practicable internal combustion turbine
would be welcomed, although it must be admitted that many cars
are now fitted with engines which leave little to be desired in this
respect. In the perfectly-balanced engine there is no dis-
tributing force acting on the frame tending to displace it on its
base.

In balancing an engine, the forces set up by the acceleration
and retardation of the moving parts are either entirely eliminated
or reduced in magnitude by —

(a) Adopting such a construction or an arrangement that they
are self-balancing.

200 MOTOR CAR ENGINEERING

(b) Adding moving masses such that their mode of motion

produces forces which oppose and counteract those set
up by the engine.

(a) and (h) will permit a perfect balance to be obtained, but (c)
only gives a partial balance, as will be seen later.

In reciprocating engines the moving parts are composed of
those having —

I. Rotating motion.

II. Reciprocating motion.

The balancing of rotating parts presents no great difficulty
and may be effected by the addition of other rotating masses,
but the balancing of reciprocating masses can only be com-
pletely performed by the introduction of other reciprocating
masses, and this it is not always desirable or convenient to do.

It will be obvious that the lighter the masses which have to be
considered, the less will be the magnitude of the forces which react
upon the frame, and hence the reduction of weight is desirable,
because it not only reduces the load on the tyres, but diminishes
vibration also, should there be any unbalanced part.

The reader should notice in the subsequent working that two
conditions are fulfilled by the perfectly-balanced engine ; namely,
that there is no resultant force and no resultant couple, and that
as the magnitude of the forces and couples is reduced, so is also
the vibration to which they give rise.

The Balance of Revolving Masses.

116. To balance a Single Botating Mass by another Botating
Mass. — If a mass M at a radius r is rotating at an angular speed
of CO radians per second, the centrifugal force produced by it is
Mo)^/' and its direction will vary from instant to instant as the
shaft rotates, but always along a radius from the axis of rotation
to the centre of the mass. The effect of this force is to tend to
displace the shaft in the direction of action, and in so doing cause
a pressure between the shaft and its bearing.

To balance this force it is necessary to introduce an equal
and opposite force by adding a mass Mi at a radius n in the
same plane of rotation, but on the opposite side of the shaft
(see Fig. 25). The line AB indicates the instantaneous direction

THE BALANCING OF ENGINES 201

of action and, by choosing some suitable scale, its magnitude
also. Clearly it must be balanced by the force represented by
the line CD.

The vectors representing forces should be drawn parallel to
the crank to which they refer and in a direction outwards from
the centre of the shaft.

It will generally be found convenient to omit the angular
speed of the shaft co from all calcula-
tions since it is common to all the
quantities considered, but where other-
wise is the case it will be indicated
in the text. It is also always assumed
that the angular speed of the shaft is
uniform.

Further, in many cases it is desirable

to reduce all masses forming the system

to a common radius, as then the radius

can be neglected. To find the mass _

Fig 25
equivalent of a mass Mx at a radius

ri, if r2 is the new radius and the equivalent is M2,

Mgrg = Ml?!
so that Ma = —^

Example : — To 6nd what mass at a radiiis 1 J ft. is equivalent to a
mass of 8 lbs. at 1^ ft.

Mjra = Mjri
Ma X H = 8 X li
Ma = 9 lbs.

117. To balance Two or more Co-planar Rotating Masses. —
Referring to Fig. 26 where the co-planar masses M, Mi, Ma,
Ms, . . . are placed at a radii r, vi, ra, rs, . . . and are rotating with
an angular velocity of <u radians per second.
The centrifugal force produced = Mw*/- -f- Miw^n -f- Maw^ra

-f MsCO^/'s + . . .

= 0)2 (Mr + Mi7-i + Mara + Mara + . . .)
For complete balance the resultant centrifugal force must =

But ft>* is not zero.
Therefore Mr + Min + Mara -h M^r^r + . . . = 0, Le. the force
polygon must close.

202

MOTOR CAR ENGINEERING

Draw the force polygon ABCDEA. The balancing force
M4r4 is the closing line AE and its direction is as shown. By
selecting some convenient dimension for r the mass required to
balance the system is found. Should the force polygon close,
without the addition of the vector AE, that is, if A coincides
with the point E, the system will be in equilibrium and not
require any balancing mass.

Care should be observed in setting out the polygon that the
forces are directed the same way round as indicated by the
arrowheads in the drawing.

118. Reference Flane. — In Arts. 116 and 117 the two systems
considered were co-planar, that is, all the masses were in the

'3*^3

Fig. 26.

same plane of rotation. But if the masses are placed in separate
planes of rotation, a couple may be introduced which will tend
to turn the shaft in a plane through its axis.

A plane of reference drawn perpendicular to the axis of the
shaft is therefore used, to which all forces are referred when
dealing with balancing problems.

It should be observed that the position in the length of the
shaft at which the reference plane is situated, is quite im-
material, but it is usual to select some plane in which a balancing
mass, if required, may be conveniently fixed. When, however,
the working has been completed and the parts balanced, another
reference plane should be taken and the couple polygon again
constructed. If the polygon does not again close when the effect
of the balancing mass is considered some error has been made in
the working. Usually, errors are traceable to the non -parallelism

THE BALANCING OF ENGINES 203

of the vectors, and occasionally to the lack of definition of their
points of intersection, but they may also arise from a mistake
in the direction in whieh they act. Where the position of
the reference plane is selected so that all the masses lie on one
side of it the vectors, representing couples, should all be drawn
from the axis of the shaft outwards towards the mass, but if
some of the masses lie to the right of the reference plane and
the remainder to the left, the direction of rotation of a couple
will be affected by its position relative to the reference plane.
All vectors representing couples lying to the left of the plane of
reference should therefore be drawn from the axis of the shaft
outwards towards the crank, and for those on the right hand side
in a reverse direction.

The force polygon, it should be noted, remains unaffected by
changes in the position of the reference plane.

Place equal masses M and Mi at radii r and n, in planes A
and B. Let the masses be diametrically opposed and let the
distance between the planes in which they are placed be a.

There will be no unbalanced force, but there are two equal and
opposite forces acting at the extremities of an arm and forming
a couple, tending to rotate the masses in the plane, and for
balance, there must be no unbalanced couple.

If there are masses M, Mi, Ma ... at radii r, n, 72, . . ., at a
distance a, 6, c, . . . from a reference plane, all rotating with
angular velocity cu radians per second then for balance the
vectors —

{M(oh'a + Miuih'ib + M2<oh'2C + . . .) =0

a)«(M + a + Minb + Marac + . . .) =0

But 0)^ is not zero.

Mra + Mi7-i6 + MaraC + . . . =
i.<?., the vector polygon must close.

119. To balance a Single Rotating Mass by Means of Two Separate
Masses which are not in the same Plane of Bevolntion. — Let the
mass M be at a radius r (Fig. 27). To balance this mass by two
separate masses Mi, Ma at radii n, r^ respectively in planes to
the right and left of the given plane and distant a and b from it.

Draw the vector AB. It is clear that the balancing masses
must produce a total force equal and opposite to AB, that is, CD.
Therefore Mr = Mi^'i + Mara = CE + ED.

204

MOTOR CAR ENGINEERING

Bat there is a further condition to be fulfilled as there must
be no resultant couple. Take a plane of reference, through Mi.
Then Mra— Ma? 26 = 0.

The position of the planes in the length of the shaft in which
the balancing masses are to be disposed will be known or may
be selected by considerations of convenience, as will also the
radii at which they are to be placed. So M, ?-, a, 72, and b will be
known and hence Ma may be obtained. In a somewhat similar
manner, by taking a reference plane through M, the balancing
mass M at a radius r may be found. These should satisfy the
equation given above, namely that Mr = Mi7'i + M/v

Fig. 27.

Example : — Two balance masses are to be placed at radii of 6 in.
and 5 in. respectively in planes 3 in. and 3J in. to the right and
left a mass of 6 lbs. at a radius of 4 in. Find the weight of the
balancing masses.

Take moments about the piano through the right hand mass.

Mra = ^f^rj)
6 X 4 X 3 = Ma X 5 X GJ

Ma = 2 l^ lbs.

Take moments about the plane through the left hand mass.

Mr{b—a) = M.rfi
6 X 4 X 3^ = Ml X 6 X 6J

M, = 2 1 lbs.

THE BALANCING OF ENGINES 205

For balance there must be no resultant force.

/. Mjr, + M,rj = Mr

M,r, + M.r, = (2 -^ x 6) + (2 J-| X 5)

= 24 = 6 X 4
= Mr.

The graphical method may be adopted by substituting the numerical
values obtained above in the vector diagrams.

It should be notod that if the balancing masses are at the same radius
and are placed in planes equally distant from the balanced mass, as, for
example, in a bicycle engine, with enclosed fly-wheels, Mr = 2Miri.
Further that a single mass cannot be balanced by one other mass not
in the same plane because of the unbalanced couple.

By a similar method of working it is clear that two masses Mi, Mg at
radii ri, rg respectively and in the same plane through the axis of
the shaft may be balanced by the single mass M at radius r. Also the
mass Ml may regarded as balanced by the masses M and M,.

120. To balance a Number of Rotating Masses which are not Co-
planar. — Let the masses be M, Mi, M,, at radii r, n, r^.

If A and B are the two planes of reference in which the two
balancing masses are to be placed if required. Using the lettering
shown in Fig. 28 and taking moments about the plane A.

Moment of force Mr = Mrc
„ „ Min = Mivib

„ „ Mb?6 in plane B = Mii'id.

Draw couple polygon, ABCDA making AB = Mre, Be =
Minby CD = Ma^aa. The closing line DA indicates the magni-
tude and direction of the force M^rj, in plane B, so DA = Mi^Vf^d.
The value of d is known, as is also the radius r^ at which the
balance mass can conveniently be placed, hence Mj, can be found.

Next draw the force diagram PQEST for Mr, Min, Mara and
Mft?-, making PQ = Mr, QR = M^n, RS = Mi7-i, ST = Mara.
The closing line TP is the magnitude and direction of the force
MaVa produced by mass at a radius ? « in plane A. Whence if ;;
is known M^ can be calculated.

Now check the working by drawing the couple polygon, by
taking moments about the plane, B, and using the values

206

MOTOR CAR ENGINEERING

obtained for M^ra from the preceding working. The couple
polygon should close.

Example: — Find what masses at a radms of 5 in. are required in
planes 4 in. to the left and right of the two end cranks of a three-
cylinder engine with cranks at 120 degrees and 6 in. apart to balance
rotating masses of 5 lbs. at each crank. Radius of crank 5 in.
(Fig. 29).

' Take moments about A, neglecting the radius, since r = 5 in. is
common.

Moment of P = 5 x 4 == 20 lbs. ins.
» „ Q = 5 X 10 = 50 lbs. ins.
„ R = 5 X 16 = 80 lbs. ins.
„ B=M X 20= 20Mlbs.ins.

Draw a couple polygon CDEFC — the closing line FC is the magni-

51'5
tude and direction of the couple 20M, from which M = -htt =^

2-5751 lbs.

Next draw the fDrce polygon GHKL making GH, HK and KG, equal
to 5 lbs. and GL equal to 2575 lbs. and parallel to the direction of the

THE BALANCING OP ENGINES

207

forces which they represent. It will be seen that the figure closes at G,
and hence the system had no unbalanced force prior to the addition of
the mass in plane B. The latter is therefore for the balance of the
couples and must be opposed by a force acting in the direction from L
to G, that is, a mass of 2*575 lbs. must be placed in plane A in the
position indicated to preserve rotational balance.

Take the moments about a new reference plane through P (say)

Moment of Q = 5 x 6 = 30
R = 5 X 12 = 60

»>

B = 2-575 X 16 = 41-2
A = — 2-575 X 4 =—10-3

Fig. 29.

Draw a couple polygon for these values, noting carefully the direction
of A. It will be found that the figure closes, and therefore there is no
resultant couple.

The Balancing op Eeciprocating Masses.

121. Primary Balancing. — So far, the balancing of rotating
masses has received attention, but there are in addition the
reciprocating masses, and these will now be considered.

In the first place it will be assumed that the reciprocating
parts have simple harmonic action which is the mode of motion
of a piston having an infinitely long connecting rod. This is
termed *' primary balancing," and takes account of the primary

208 MOTOE CAE ENGINEEEING

forces and primary couples only, neglecting the eflfect of the
connecting rod.

It may here be desirable to correct an impression which is
sometimes held, that the variation in the pressure within the
cylinder causes a reaction on the engine frame and thus pro-
duces engine vibration. If the total pressure on the piston is P
and the moving parts are assumed to be without mass, so that no
force is required to produce acceleration, the force P acting
through the connecting rod transmits a force of equal magnitude
to the crankshaft bearings, tending to displace them in the
direction in which the piston moves.

The total pressure P within the cylinder^lso causes a thrust
on the cylinder head in the opposite direction to the motion of
the piston which is transmitted through the cylinder casting and
framing, and opposes the force acting along the connecting rod to the
crankshaft bearings. Hence, the pressure acting within the cylinder
produces no vibration of the engine upon its base. There is, how-
ever, a small oscillation of the engine and chassis frame upon the
springs and about the axis of the crankshaft due to the variation of
torque, but its analysis is somewhat difficult, if it is not altogether
impossible, of exact solution. Its magnitude will obviously
decrease as the uniformity of torque increases, that is as the
number of impulses increase, but it is comparatively unimportant
except when the period of oscillation synchronises with the
natural period of the frame and the parts attached thereto upon
the springs.

But as the reciprocating parts have mass, some force is
requked to accelerate and retard them, and this must be supplied
by the pressure acting upon the piston. For the first half of the
stroke the parts are accelerated, and for the second half decele-
rated, therefore during the first half stroke the pressure on the
piston transmitted to the crank will be diminished by an amount
equal to that necessary to accelerate the parts, while in the
second half it will be increased by that given out by their
retardation.

Since, however, the thrust on the cylinder head will always bo
that due to the pressure within the cylinder alone during the
first half of the stroke there will be an unbalanced force tending
to displace the engine outwards from the crank and on the latter
half of the stroke, towards the crankshaft, resulting in the

THE BALANCING OF ENGINES 209

vibration of the engine on its supports in unison with the
movement of the piston, but in an opposite direction.

122. Primary Balance of a Single-Cylinder Engine. — Assuming
simple harmonic motion, the instantaneous force required to
accelerate the reciprocating parts is Mco^r cos 6 where M is the
massj 0) the angular velocity in radians per second, r the radius
of the crank in feet and is the angle through which the crank
has turned from the inner dead centre. The expression will be
negative, when the value of cos 6 is negative.

Let the reciprocating masses be transferred to the crankpin.
Then the projection of this motion of the rotating masses on any
fixed axis, as the line of stroke, is simply harmonic. The centri-
fugal force produced by the rotation of these measures is Mo)^;-,
which, on being resolved in the line of stroke and at right angles
to it in the plane of rotation> gives Ma>^r cos in the first direc-
tion and McD^r sin in the second. If, therefore, a mass is
added to the shaft to balance the mass of reciprocating parts
assumed to be concentrated at the crankpin, the parts will be
balanced in the line of stroke, but an unbalanced force will be
introduced having a magnitude of Mo)^/* sin 6^ in a direction at
right angles to the plane of reciprocation. This new force will
undergo similar changes in value to that which the force required
to accelerate the reciprocating parts was subject, its direction
only being altered, and although permissible in many classes of
work, it is not desirable in automobile engines.

Therefore, where complete primary balance cannot be effected,
instead of fully balancing the reciprooating masses in the line of
stroke, they are generally only half-balanced, that is, only one
half of the reciprocating masses are transferred to the crankpin
and balanced.

From the preceding it should be clear that it is not possible to
completely balance reciprocating masses by rotating masses, and
the importance of keeping down the weight of the reciprocating
parts to the minimum consistent with good design should be
readily apparent.

The methods employed in balancing the reciprocating masses
when transferred to the crankpin as imaginary rotating masses
will be as have already been indicated in Arts. 116 to 120.

Example, — Find the magnitude of the instantaneous unbalanced
force, when the crank of a single-cylinder engine, running at 1,200

M.C.E. P

210

MOTOR CAR ENGINEERING

BiO

revolutions per minute, makes an angle of 60 degrees with the line of
stroke, if the engine is fully balanced for primary forces. Weight of
reciprocating parts 3 lbs. and radius of crank 2 J ins.

Force = MwV sin 6

3 (1,200 X 27r)2^ ^ _.
= 3-2^2^-^60 ^Xt|x-«66

= 266 lbs.

128. Primary Balancing an Engine with more than one Cylinder. —
It has been seen that the force required to accelerate reciprocathig

masses moving with simple
harmonic motion is MwV
cos 6.

This IB also the component
of the centrifugal force of the
reciprocating masses in the
plane of reciprocation when
transferred to their crank-
- pins, and therefore the
resultant effect upon the
frame of a system of
reciprocating masses is the
summation of the com-
ponents of the centrifugal
forces of the reciprocating
masses when transferred to
the crankpins.

Cane 1. When system is balanced for rotating forces and couples. —
Suppose a system of reciprocating masses M, Mi, Ms, Ms are
connected to the cranksliaft shown in Fig. 80, and are all at a
radius r. With the masses, angles and dimensions given the
system is balanced for rotating forced and rotating couples.
Draw the force polygon PQRS and a line parallel to the plane of
reciprocation AB.

Project the points P, Q, R, S on to MN.

Then o, oi, era, a^, are the respective components of the cen-
trifugal forces in the plane of reciprocation AB, their direction
being as indicated, and since a + ai — ag + ^s = ^be effect of
these forces in this plane is also zero.

Similarly, if another lino be drawn at right angles to the line

THE BALANCING OF ENGINES 211

MN, the summation of the projections from the pointa P, Q, E
and S on to it will again be zero.

If the cranks are rotated the force polygon will still close,
although the magnitude of the compoaeots a, Q], n^ and a^ will
vary, and therefore in any position of the crankshaft there will
he no unbalanced primary force.

In a similar manner, and for similar reasons, if the couple
polygon is drawn and is found to close, there will be no primary
couple unbalanced.

Cote 2. When system is not balanced for rotating forces and
couples. — It will have been observed that the system considered
. was already balanced
for revolving forces * *• * '**

and couples, an d
although this is the
case in many auto-
mobile engines, it is
obviously not always
so.

As an example, con-
sider a two - crank
engine with cranks at
180 degrees (Fig. 31).

Let the weight of the „ ^, "

reciprocating parts be

4 lbs. per cylinder, radius of crank 3 in., distance between
centre line of cylinders 6 in., and assume that the engine speed
is 1,200 revolutions per minute.

Transfer the mass of the reciprocating parts to the crankpin
and draw force diagram. It will be seen (Fig. 25) that diagram
closes as the force from -mass at A acts in the opposite direction
and is of equal magnitude to that from the mass at B, and hence
there is no unbalanced force.

Next take a reference plane through one of the cranks, say
at A, and construct couple diagram. This shows that the couple
of 245 lbs, ft. is unbalanced, so that to fully balance it a mass
most be introduced which will produce a couple of 245 lbs. ft.
in the opposite direction to that from the mass at B when rotating
at 1,200 revolutions per minute.

Hence, the equivalent of a mass of i> lbs. at a radius of 3 in,

p a

2X2 MOTOlt CAK ENGINEERING

may be placed in the plane of rotation of B, or be suitably dis-
posed on the two sides of it (see Art. 119) and on the opposite
side of the shaft to the balanced mass.

By taking another reference plane through B it will be found
to be necessary to add an equal mass- in a similar position with
regard to the crank A.

These new masses will, however, be rotating, and the com-
ponent of the centiifugal force in the line of stroke will balance
the masses which have been assumed as concentrated at the
erankpin, consequently there will still be an unbalanced couple

at right angles to the plane of recipropation equal to MtoS-
sin ea.

This will attain its maximum value when sin 9ts a maiimum,
that is, when =: 90 degrees, and the expression then equals 245 Iba.
ft. By half -balancing the reciprocating parts (see Art. 122) the
magnitude of this couple may be reduced to a maximum of
122 '6 lbs. ft., and there will still remain an unbalanced couple
in the plane of reciprocation of equal maximum value. The
masimam value of the couple in one plane will, however, only
occur when the couple in the other plane is zero.

This example also illustrates the importance which must be
attributed to the lightness of the reciprocating parts.

But a complete primary balance may be secured in another
way, namely, by giving the two additional masses reciprocating
motion from two added cranks. These two cranks may either

THE BALANCING OFj ENGINES 213

act as " bob-weights," whose sole function is to produce balance,
or they may serve as the reciprocating parts of two other working
cylinders.

Proceeding as indicated by the latter method the additional
cranks may be arranged in the same plane of rotation as the
balance- weights, bat it will be seen that by placing both on the
same side axially of £ the conventional four-cylinder arrangement
is obtained if the first crank is placed on the same centre as B
and the second on the same centre as A (leee Fig. 82). From
considerations of uniformity of torque the cylinders in which
G and D reciprocate will be of similar dimensions to A and B,
and therefore their masses will be the same as will also the
distance between G and D.

From the force diagram it will be seen that there is no
unbalanced rotating force.

Let the distance between B and C he d and take moments
about B.

Moment from force at A = 490 X ^

„ „ C = 490 X d
„ >, D = 490 X (d + i).

The sum of the moments must be zero. Hence,

(490 X i) (490 Xd)- 490 (d + i) = 0.

A similar result may be obtained from the couple diagram if
a value for d is assumed, and hence it is clear that complete
primary balance is secured by making d any convenient dimen-
sion, as since the new masses reciprocate there will be no force
or couple at right angles to the plane of reciprocation.

In the preceding work on primary balancing the method by
which the balancing masses for the reciprocating parts only may
be estimated has been indicated, the revolving masses must be
separately balanced, and it is usual in so doing to place one mass
in each of the planes of rotation in which the masses for. the
balance of the reciprocating parts are secured. The two masses
in either plane may then be compounded, as they constitute
two forces acting at a point and in the same plane, and their
resultant is the mass which is actually placed in the plane.

It should be observed that it is not possible to compound two
masses which are in separate planes of rotation in a similar
manner.

214 MOTOR CAR ENGINEERING

124. The Eeciprocating and the Eotating Parts. — The piston
complete and gudgeon pin have a purely reciprocating motion,
and the crankpin and crankwebs have a purely rotating motion,
but one end of the connecting rod reciprocates with the piston
and the other rotates with the crank. To find in what manner
the rod should be divided it is usual to support it upon balances
placed at the centres of the bearings and take the readings at
each end, the weight which is treated as rotating being shown
at the big end, and that which is reciprocating at the gudgeon
pin end.

Or if AB is the length of the rod, A being at the crankpin end

and C its centre of gravity along its length — then j^ x mass

BC
is considered as reciprocating and j^ X mass as rotating.

Professor Dalby has suggested the following method. If P is
the centre of percussion and the nomination of the parts are
as above, then the rotating masses are taken to be equal to

YTs X mass, and the remainder as reciprocating masses.

These dimensions do not completely account for the motion of
the connecting rod since there is a couple acting in a transverse
plane, produced by the angular acceleration of the rod about its
mass centre. This couple tends to rotate the engine about an
axis parallel to the axis of the crankshaft, but is generally of
little magnitude, and not infrequently the arrangement of cranks
is such that the couples neutralise each other.

125. Secondary Balancing. — Hitherto, it has been assumed that
the motion of the reciprocating parts is simply harmonic, and
this would be so were the connecting rod infinitely long : but as
the ratio of length of the connecting rod to crank decreases so does
the actual motion deviate from that which has been assumed,
consequently the acceleration differs from a>V cos owing to the
obliquity of the connecting rod.

The force required at any instant to accelerate the reciprocating
parts is given by an expression which is of little service in
balancing problems, but it can be replaced by the following
Fourier Series, in which the terms diminish rapidly in magnitude,
and this is always employed in investigation.

THE BALANCING OV ENGINES 215

( T 7^

Force = Mio^r (cob ^ + rcos 2^ — J ^5 ^^^ ^^ +

cos 6^

• • • • I

128 P

where r is the radius of the crank, 1 the length of the connecting
rod. The above expression is not quite exact, as the second term,
for example, should be —

(j + i ja • • • •) cos

while the other terms also neglect certain quantities, but it is
sufficiently so for all practical purposes.

The first term of the series is MwV cos ^, the force required
to produce acceleration with simple harmonic motion and which
has been considered in primary balancing. The second term is

— :j — cos 2^, and when this is considered the operation is termed

lif ft) r
" secondary balancing." The remaining terms are — r— tb cos 4^,

^^^ 7^ COS 6^, etc., and are known as the inertia forces of the
128 P

fourth, sixth and higher orders respectively.

When the first and second terms of the series are satisfied the
engine is said to be balanced for primary and secondary forces
and couples, and it may be added that unless an engine has
complete primary balance, it is unnecessary to consider its
condition as to balance for secondary effects, or those of the
higher orders. Generally, it will be found that the inertia
effects of the fourth and sixth orders may be neglected altogether
because of their extremely small magnitude in the modern
engine.

Confining our attention to primary and secondary balance, the
instantaneous force in the line of stroke required to accelerate
the reciprocating masses is —

Mco^r f cos ^ + ^ cos 2^ ) .

Taking the first term Mco^r cos ^, this is the resolved part
in the line of stroke of the centrifugal force of a mass M
at a radius r rotating at an angular speed of o) radians per
second.

216 MOTOE CAR ENGINEERING

Similarly, the second tarm is —

M^\o8 2^ = M4^co8d = ^M(2o.)Vcos2d

i 41 41

and is therefore the resolved part in the line of stroke of the
centrifugal force of an imaginary mass — M at a radius r

rotating at an angular speed of 2w radians per second. On
account of the obliquity of the connecting rod, there is, therefore,
a second force having twice the frequency of the primary force,
and if an attempt were made to balance this it would be necessary
to introduce another crank revolving at twice the speed of the
main crank.

The effect of the inertia forces of the fourth and sixth orders
may be treated in a similar manner, and will be found to be
equivalent to that form of imaginary cranks rotating at four
times and six times the speed of the engine crank.

The centrifugal force produced by the rotation of the mass in

the manner described for secondary forces is — = — , and its

direction is outwards from the centre of the shaft along the
radius of the imaginary crank. Its resolved part in the line of

stroke is — ij — cos ffy and at right angles thereto is — z —

sin 0, where is the angle through which the imaginary crank
has turned from the inner dead centre, i.e., twice the angle turned
through by the main crank. It will be observed that the force

- - — is the primary force multiplied by the ratio of the crank

to connecting rod -. The problem may be attacked in the

graphical manner previously described for primary balance,
then, if the force and couple polygons close, the engine under
examination is balanced for primary and secondary effects, but
if not, the magnitude and direction of the unbalanced force or
couple is ascertained.

But the following method is sometimes preferred on account
of the liability of error creeping in when drawing the vectors for
secondary forces and couples. When the graphical method is
adopted, separate diagrams should be drawn for the main crank

THE BALANCING OP ENGINES

217

when dealing with primary balancing and for an imaginary
crank rotating at twice the speed when considering the secondary
balance. Thus, when No. 1 crank has turned through an angle 0^
the imaginary crank for the reciprocating masses assumed to be
concentrated at No. 1 crankpin will be at an angle of 2d with
the dead centre, the imaginary crank for the reciprocating mass
of No. 2 cylinder transferred to No. 2 crankpin will be at an
angle of %0 + a) with the line of stroke, and so on. The
example below will be examined for both primary and secondary
effects.

126. The Balance of a Siz-cylinder Engine with Cranks arranged
at 120^ as shown in Fig. 33. — The masses of all the recipro-

cating parts will be taken as equal and of magnitude M at
radius r.

Resolving the centrifugal forces produced by rotation in the
line of stroke and at right angles thereto, if there is no resultant
force we have —
Primary force in the line of stroke "

= MwV I ®^s ^ + ^^s (^ + a) + cos (d + ai) + I _ ^

1 cos (Q + ai) + cos (5 + a) + cos d j
It will be seen that the cosines of the first three angles are
repeated, so it is only necessary to multiply the quantity outside
the brackets by two and delete the last three quantities inside the
brackets.

218 MOTOR CAR ENGINEERING

Secondary force in the line of stroke

a.^

0)-/

^ .cos 26 + cos 2 (^ + a) + cos 2 (^ + ai)] = 0.
Primary force at right angles to the plane of reciprocation

= 2M<oV sin (9 + sin (^ + a) + sin {0 + ai)

= 0.

Secondary force at right angles to the plane of reciprocation

2M<oV

sin 2(9 + sin 2 ((9 + a) + sin 2 ((9 + ai)| = 0.

Select a reference plane at a distance a, to the left of the
first crank and taking moments ahout it.

Moment of Primary force in line of stroke

= Mw^rj^^ ^^® + a^ cos (^ + a) + as cos {0 + ai)| __ ^
1+ 04 cos (d + tti) + as cos (<? + a) + ttg cos ^ J

Moment of Secondary force in line of stroke

= Mft)V i^^ ^^® 2^ + 02 cos 2 (^ + a) + aa cos 2 (^ + aO) _. ^^
I + a^ cos (^ + ai) + as cos 2 (^ + a) + ae cos 25)

Moment of Primary force at right angles to plane of reciprocation

= Ma)«r \ ^^ ^^^ ^ + «2 sin (5 + a) + as sin (^ + ^i) +) -., q
1 a\ sin (5 + ai) + as sin (^ + a) + a^ sin 5 J

Moment of Secondary force at right angles to the plane of
reciprocation

Ma>^r*

ai sin 25 + a^ sin 2 (5 + a) + aa sin 2 (5 + aj 1 __

+ 04 sin 2 (5 + aj) + a^ sin 2 (5 + a) + a^ sin 25 j

These then are the eight equations which must be satisfied if
any engine is in perfect balance for primary and secondary
forces and couples, no matter what the number of cranks may
be.

Consider the conditions when the angle is 50 degrees, the
distance apart of the cranks 6 in., and the reference plane 4 in. to
the left of No. 1 crank. As the mass M, radius r, length of
connecting rod 1 and the angular speed co is common they may be
neglected without affecting the result if the parts are completely
balanced, but will require to be considered. Find the magnitude
and direction of the unbalanced force and couple, if not
balanced.

THE BALANCING OF ENGINES 219

The left-hand side of the first eqaation is then

= cos 50° + cos 170° + C03 290° + cob 290° + cos 170° +
cos 50°

= 0-6428 — 0-9848 + 0-8420 + 0-3420 — 0-9848 + 0-6428
= 0.

The left-hand side of the second equation

= cos 100° + cos 840° + cos 580°
— 0-1737 + 0-9397 — 07660
= 0.

The left-hand side of the third equation
= sin 50° + sin 170° + sin 290°
= 0-7660 + 0-1736 — 0-9396
= 0.

The left-hand side of the fourth equation
= sin 100° + Bin 840° + sin 580°
= 0-9848 — 0-3420 — 06428
= 0.

The left-hand side of the fifth equation

= 4 cos 50° 4- 10 cos 170° + 16 cos 290° + 22 cos 290° +

28 cos 170° -t- 34 cos 50°
= (4 X 0-G4-28) — (10 X 0-9848) + (16 X 0-3420) + (22

X 0-3420) — (28 X 0-9848) + (34 X 0-6428)
= 2-5712 — 9-848 + 54720 + 75240 — 275744 + 21-8552
= 0.

The left-hand side of the sixth equation

= 4 cos 100° + 10 cos 340° + 16 cos 580° + 22 cos 580° +

28 cos 340° -t- 34 cos 100°
= (4 X - 0-1737) -t- (10 X 0-9397) -|- (16 X - 0-7660) -f-

(22 X - 0-7660) + (28 X 0-9397) + (34 X - 0-1737)
= — 0-6948 + 9-897 — 12-256 — 16-852 -|- 26-3116 — 5-9058
= 0.

The left-hand side of the seventh equation

= 4 sin 50° -I- 10 sin 170° + 16 sin 290° -|- 22 sin 290° +

28 sin 170° + 34 sin 50°
= (4 X 0-7660) + (10 X 0-1736) -|- (16 X — 09396) + 22 X

— 0-9396) + (28 X 01736 + (34 X 07660)
= 3-0640 + 1-736 — 150336 — 20-6712 + 4-8608 + 26-0440
= 0.

220 MOTOR CAR ENGINEERING

The left-hand side of the eighth equation

= Bin 100° + 10 sin 340° + 16 sin 580° + 22 sin 680° + 28

sin 340° + 34 sin 100"
= (4 X 0*9848) + (10 X - 0*3420) + (16 X - 0*6428) +

(22 X - 0*6428) + (28 X — 0*3420) + (34 X 0*9848)
= 3*9392 — 3-420 — 102848 — 14*1416 — 9*576 + 33*4882
= 0.

Another position may be selected, if desired, but it will always
be found that a six-cylinder engine with cranks at 120 degrees is
balanced for primary and secondary effects provided that the
masses are the same in all cylinders and the weight is distributed
in a similar manner in all cylinders. The cause of the vibration
which is sometimes expressed in a six-cylinder engine is largely
due to the weights of the moving parts in the various cylinders
being uniform.

A similar method of treatment may be applied to any number
of cylinders for primary or secondary balance and the working
that has been shown should enable the reader to make the
investigation.

For the complete investigation of the problems of balancing
to which the preceding can only be considered as the introduction
because of the extensive nature of the subject, the reader is
recommended to study the works of either Dalby or Sharp
entitled " The Balancing of Engines," in both of which the
subject is fully treated. He may also refer to the Transactions
of the Institution of Nai'al Architects, Vol. XLIIL, and the Pro-
ceedings of the Institution of Civil Engineers, Vol. CLXVIII.
The latter contains a paper on the '' Estimation of the Un-
balanced Forces in Multi-Cylinder one-crank Engines." For
the balancing of engines with oflf-set cylinders see Automobile
Engineer for November, 1910.

CHAPTER XI

CRANKCASES AND aEARBOXES

127. Materials, etc. — The material commonly used for crank-
cases and gearboxes is an aluminium alloy of between 11 and 14
tons ultimate tensile strength, although cast-iron is occasionally
employed, more especially for gearboxes. Alloys of aluminium
having a higher tenacity are available, but are unfortunately
much more brittle and less reliable in positions such as these,
where shock and fluctuating stress is experienced. In getting
out a design for a crankcase or gearbox, the object in view is to
obtain as rigid a construction as possible— strength is then
sufficient. Therefore, because of this, as well as because of the
more or less extremely complicated construction necessarily
employed and the difficulty in determining the actual loads
which the castings are required to withstand, the design is
worked out from experience, and affords the designer ample
scope for his faculties. .

Attention is drawn to the importance of employing bolts
whenever practicable, instead of studs if aluminium is used, on
account of the facility with which the thread in the casting is
stripped, partly because of the imperfect thread obtained in
tapping. To overcome this difficulty the casting is sometimes
tapped to a larger dimension of fine thread and a screwed bush
or ferrule inserted therein, the ends of which are riveted over
and then tapped out to the same size as the stud. This is,
however, an expensive method, and bolts are more satisfactory,
but are subject to the disadvantages that it is necessary to hold
the head when dismantling a part, and that they drop out when the
nut is removed. These may be avoided by screwing the bolt up
to the head and screwing it in the tapped hole in the casting
through which it passes from the inside. Whenever studs are
screwed into aluminium, the length of the screwed part should
be never less than twice the nominal diameter of the stud.

222 MOTOR CAR ENGINEERING

128. Crankcase Construction. — The cross- sectional dimensions
of the crankcase are determined almost entirely by the space
required to clear the cranks and connecting rod ends and for the
placing of the camshafts, skew shafts, etc., while the overall
length is similarly dependent upon the cylinder, crankshaft and
timing gear requirements. It is obviously desirable to keep
down the size of the crankchamber as much as practicable to
obtain ample clearances, but in doing so the means of access to
the various parts must be studied, and the facility with which
such a casting can be made.

The top plate'should be made of ample thickness in order that
rigidity of the cylinder seating may be obtained, and preferably
the bolts for the main bearings should be carried through pillars
extending from the top to the bottom of the crankcase, the bolt
heads being recessed into the casting so as to present a flush
surface for the cylinder. If possible these bolts should also
secure the cylinders in place, and if so, it is advisable to form a
collar upon the bolt so that it will recess into the top plate and
keep the bolts and crankshaft in position even when the cylinders
are removed. There are usually baffle plates fitted underneath
the cylinder to prevent the excessive lubrication of the piston, but
not infrequently these are cast integral with the casing, a space
being left for the rod to pass through. The inner edges of the
holes in the top half of the crankcase should be stiffened round
their circumference by a ring of metal, and the oil baffles should
slope towards the slot so as to prevent the accumulation of oil.

The sides and ends of the case should not be made less than
^^ in. (8 mm. thick), but the actual dimension will depend
upon the size of the casting, the methods of support and the
extent to which ribbing is carried out. Ribbing and webbing is
of great service, not so much because it strengthens the part, but
by stiffening it, it prevents undue flexure, high stresses and
wear. For these reasons the main bearings should have good
webs attaching them to the sides and top, and all corners should
be well filleted and webbed. If any form of splash lubrication is
employed it will be necessary to provide caps or pockets at the
bearings. These should be of couple capacity, and where two oil
holes are led to the journals a common pocket should be made,
not one each side of the web, so that as long as oil is thrown up
against one side the bearing will be lubricated. The minimum

CRANKCASES AND GEARBOXES 223

thickness is limited by the necessity for a good, sound casting — if
very thin there is a great danger that the metal will not flow
freely through the mould. When the casting is very large and
thin it is often of service to cut triangular pieces of the same
metal as that from which the casting is to be made, and fit them
into the mould at the corners instead of casting the webs ; these
pieces of metal will then join up with the main body of metal
and tie the sides together.

It is not unusual, in order to eliminate the use of piping for
lubrication purposes, either entirely or partially, to arrange that
the oil conduits shall be in the casting itself. This may be
effected by swelling out the metal in the locality in which it is
desired to place the duct and drilling a hole from end to end, the
ends being plugged as necessary and bosses arranged, and nipples
in the length of the hole as convenient for taking off the leads to
the bearings. These holes should always be drilled because of
the difficulty of removing the core used in casting, which might
find its way into a bearing. In the top half of the crankcase it
is also usual to arrange for the camshaft bearings. These are
generally of simple construction, and consist of plain holes in the
webs to the bearings or separate webbed supports, in which the
phosphor bronze bushes may be placed, the latter being held in
position by pegs or by set-screws let in from the outside. In some
cases the camshaft is lubricated by splash from the crankcase,
but occasionally a separate trough is arranged for into which the
cams may dip. Arrangement may also be necessary for carry-
ing the shafts driven off the camsliaft for driving the pumps or
magneto. These will always be run in bearings, pinned so as to
prevent rotation and end movement, fitted to bosses, and if a
worm or skew gear is provided, will be arranged with a phosphor
bronze collar thrust bearing. If the shaft is vertical, or nearly
so, it is a good plan to form a pocket in which oil may collect
around the thrust collar, as this ensures an adequate supply of
lubricant.

The provision of inspection doors in the side of the crankcase
is commendable, but whether they can be arranged for or not
will depend upon the method of support and the depth to which
the engine is sunk in the frame. But in all cases where they
are fitted it is desirable that their removal shall be as easy as
possible, and not involve taking off a large number of nuts.

224 MOTOR CAR ENGINEERING

Means are necessary for the attachment of the magneto and
pumps, and the best method of so doing will be determined largely
by the manner in which the engine is suspended. If side arms
or a long side plate is fitted it will probably be simplest to place
these auxiliaries lengthwise at the side of the engine, but this
will also depend upon the manner in which they are driven.
With a skew-driven shaft at the front of the engine, the magneto
and pump can be very conveniently arranged there, leaving the
sides perfectly free. As to whether it will be best to make a
separate bracket and bolt it to the case or to cast a shelf integral
with the crankcase must be determined when the actual construc-
tion at the end is known. The supports for the fan should also
receive attention, as it may be carried on a bracket placed on top
of the crankcase or secured to the cylinder casting. It is always
desirable that a vent pipe and an oil-filling pipe should be pro-
vided for, the former to prevent the creation of a partial vacuum
or a pressure above the atmosphere in the crankchamber by the
pistons, which has a detrimental effect upon the lubrication of
the engine ; and the latter, to enable oil to be introduced easily
and immediately. Too often it is found that the oil supply
arrangements are altogether inadequate, and require to exercise
a deal of patience in renewing the lubricant, especially if it is at
all viscous.

The bottom half of the crankcase can be made thinner than
the top if suspended from the latter as is, now practically
general, but in any case it is not altogether a desirable end since
the provision of a sound casting, although imperative, is rendered
more diflBcult. If the ends only are cast, the body may be of
sheet metal and riveted to them, the sump for oil being pre-
ferably cast separately and secured by riveting. This is not,
however, any great advantage, except where very light weight is
essential, besides which it is rather more expensive and less con-
venient for the arrangement of fittings.

The bottom half acts as a sump for oil, and its actual con-
struction will depend upon the type of lubrication afforded, but
in all cases the oil should be able to drain either to one end or to
the middle, the bottom being sloped so as to facilitate this, even
when ascending a hill. A special sump may be provided from
which the oil may be drawn by the pump, or there may be a
trough which may extend to more or less the full length of the

CRANKCASES AND GEARBOXES 225

engine (see Figs. 4, 5, 7, and 9). This is usually secured by
nuts and bolts to the crankcase for removal when cleaning out.
It will generally be found desirable to place a grid over the sump
or trough having a large area, and this may be in addition to the
filter in the lubricating system. An oil level cock or gauge glass
and an oil drain cock is also essential. Oil coolers are sometimes
fitted so as to enable the oil to retain its lubricating properties,
after being heated during its passage through the engine. Ribs
placed on the exterior of the sump assist in achieving this purpose.
. The lubricating systems are, however, considered in Vol. I.,
Chapter XIX., and receive further attention in Arts. 131 — 184.

Attention id especially necessary to see that the construction at
the ends of the case in the vicinity of the bearings will prevent
the exit of oil or the entrance of grit and dirt. These should be
formed so that the casing extends slightly beyond the actual
bearing, and the oil thrower (if fitted), in order that any oil
passing through the bearing will drain back into the sump. The
joint between the top and bottom halves of the crankcase is
important and so far as is practicable (and this can nearly always
be arranged for), should be machined all over so as to be quite
tight to prevent leakage of oil which would give such a dirty
appearance to the engine.

The timing* gear should be totally enclosed by an end plate,
the dimensions being kept as small as possible so as to avoid a
cumbrous arrangement, and the oil should be able to run directly
back from the timing case to the crank-chamber. Bearings for
gearshafts should not, if possible, be supported by the outer
cover on account of the probability of bad alignment.

129. Gkarboz ConstructioiL. — Here again the general shape is
determined by the space required for the wheels and the
operating gear, and convenience of access. Every endeavour
should be made to reduce the lengths of the shafts, so as to
obtain greater rigidity for any given diameter, as the flexure of the
shafts is one of the causes of inaccurate contact of the teeth, and
therefore noise. One may say that the practically universal
arrangement is for the primary and secondary shafts to lie in a
horizontal plane, and for the reverse pinion to be placed below
the centres of these shafts. The gearbox is usually cast in one
piece, the bearings being formed in bosses or other suitable
supports on the ends, while an inspection lid is provided at the

M.C.E. Q

226 MOTOR CAR ENGINEERING

top. The top cover should be as large as can be conveniently
arranged in order to afford easy access to the interior of the box,
although with some designs this is a somewhat dilBcult matter;
owing to the arrangement of the striking gear. It should be
secured by as few butterfly nuts as will effectively exclude dust
and prevent the exuding of lubricant, and a plug of not less than
1 in diameter (25 mm.), should be provided at the bottom at
the lowest portion for draining purposes when cleaning out.
Preferably, there should be also a short vent pipe to allow air
to escape when the box warms up, and this can be so designed
that it will serve also as a filler. Caps should be provided over
the ends of the bearings of the lay or secondary shaft and glands
at the ends of the other shafts to retain the lubricant (see
Fig. 4). To prevent any possibility of grit, chips from the
wheel teeth or other foreign matter entering the bearings it is
advisable to provide some form of protector, and this may consist
of thin shield plates of metal fitted on the shafts close up to the
bearings.

In most designs, ball-bearings are employed for the main shaft
bearings, two being provided at one or both ends in some designs
(Figs. 54 and 55), especially for the short length of a divided
shaft, in order to obtain stability, and it is well to place them as
far apart as possible. Where ball-bearings are used it is
necessary to make the housings for the bearings of the lay shaft
of such a diameter that it may be readily withdrawn through the
aperture after the second speed wheel has been disconnected.
This is sometimes popsible with the diameter of outer rail
employed, but it is preferable to use a separate casting to carry
the bearing and withdraw the bearing and the lajshaft, or a portion
thereof, entire without disturbing the bearing or the shaft. Set
screws or hardened steel buttons are sometimes fitted to keep the
layshaft from moving endwise, and ball thrusts for a similar
object on the primary shaft.

Generally, the whole of the striking gear is placed on one side
(that nearest the driver), and actuated from the upper part of the
box. The ends of the selector rods should be enclosed, care being
taken to see that there is ample room for the full movement of
the rods. Provision must also be made for the recesses in which the
plungers and selector rods slide, and for the locking gear. These
bearings or guides should be bushed, as, indeed, should all working

CRANKCASES AND GEARBOXES 227

parts of a similar nature, so as to allow of smooth working and easy
repair. Occasionally these parts are carried by a gunmetal
casting bolted to the gearbox, in which case bushing is not so
imperative since the bearings can be bored out to receive the
bushes when worn. When the selector fingers are attached to
guides sliding on fixed bars, a most desirable arrangement, as
leakage of oil or grease is reduced considerably, bushing is un-
necessary. Leakage may be almost entirely avoided by making
all bushes with blank ends, a recess being turned at the extreme
end of the bush, and the bushes being bolted to the case.

Not infrequently the brake actuating gear is arranged in the
top or side of the gearbox, in which event the casting should be
thickened up in the vicinity and the rim of the inspection hole
well ribbed to prevent undue distortion.

General Note. — All ribbing, webbing, bosses, etc., should
wherever possible be placed on the interior of the casting since this
not only permits of a smooth exterior that is pleasing to the eye,
but also prevents that accumulation of dirt that disfigures the
part and possibly works into a bearing. Where facings are pro-
vided for Beatings, they should stand slightly proud of the surface,
just sufficient to give the necessary thickness for studs or bolts in
order to facilitate machining operations. Here again, however,
regard must be paid to the foundry requirements.

So far as is practicable, all holes to be drilled or bored should be
arranged so that they may be machined in either a horizontal or
vertical position for convenience in operation and cheapness in
manufacture.

180. Engine and (Gearbox SaspenBionB. — It should be regarded as
a cardinal point that the suspension of the engine and gearbox
must be such as will render them completely immune from any
distortion that occurs in the framing. Too often one sees designs
in which the attachment is such that the crankcase and gearbox
cannot fail to be subjected to considerable twisting stresses, while
the relative motion between the engine and gearbox necessitates
the provision of some flexible connection. Not that even in the
ideal form should the universal joint be eliminated, because it
permits of a little adjustment to compensate for any deficiency in
the alignment and subsequent wear, but it is clear that if the
actual need for such is reduced, so will also be the wear, and the
fractional bosses must also be minimised.

Q 2

228 MOTOR CAR ENGINEERING

In this sense, the ** three-point suspension " is advocated, not
for the engine alone, but it should be made so as to embrace the
engine and the gearbox — the unit construction. Thereby correct
alignment is easily obtained and maintained, the friction and
wear are reduced, and less trouble is experienced with joints and
bearings in the engine and gearbox, albeit, it is rather more
expensive (although the extra cost may be compensated for by
the lower cost of assembling), and the careful selection of the
materials and the design employed are imperative if freedom
from breakdown and ready means of access are to be ensured.

Suspension may be broadly said to be carried out in three
different ways —

(a) By the unit system.

(b) By supporting the engine and gearbox on an underframe.

main frame.

The advantages of the system (a), and some of its disadvantages
have already been mentioned, there remains one other that should
be referred to, namely, the difficulty of preventing some sagging
of an aluminium alloy casting taking place between the points of
supports. This is a very real defect, and becomes more pro-
nounced as the size of the engine increases, so that many manu-
facturers hesitate to adopt such a system for this reason, apart
from the doubt that is felt in the minds of some designers as to
the ability of aluminium to withstand the heavy loads that are
experienced in practice, even though the probable stress may be
small. It is really the uncertainty of the distribution of stress.

With the unit system of construction the front of the engine is
carried in a hollow trunnion in the front cross-member, the
starting handle passing through the inside of the trunnion, while
the two lugs carried on the gearbox secure the rear end to a
tubular or a pressed steel girder between the two side frames.
In another form, the front of the crank-chamber is provided with
arms that rest upon the side frames, and a single bracket attaches
the gearbox to a cross girder just behind and above the gearbox.
There are variations of these which differ only in the method of
attachment and not in the actual principle involved, as for
example, in the Lanchester car, where brackets are taken off the
sides of the gearbox and hinged upon the side members. The
gearbox and the crank-chamber are usually separate castings

CRANKCASES AND GEARBOXES 229

bolted together even in the smallest sizes, sometimes entirely
closed with an inspection door at the top, and often open from
above between the engine and the gearbox, so as to afford
immediate access to the clutch, etc.

The underframe is probably that which is most in evidence at
the present day, and rightly so, since the merits of the anit
system can be obtained without its demerits. Here the engine
and gearbox are carried upon either a U-shaped framing or upon
a pair of longitudinal girders. The former is preferred, since the
three-point suspension is assured, the front end (the bottom of
the U) being attached io a cross-frame in front of the engine
and the open ends of the U to a cross girder at the rear of the
gearbox. Sometimes the bottom end of the U is not rounded
but the sides converge to the centre of the cross-girder. In the
two-girder form each girder comes as close to the centre of the
car as possible, but hardly sufficiently to isolate the engine, etc.,
from all frame distortion, so that in this respect it is inferior.
The two girders may, however, be carried at one end, usually
the front end, by a bracket, the centre of which is secured to the
cross-girder, in which event the arrangement corresponds closely
with the U girder type. The methods of attachment of the
underframe vary considerably, not only in detail but in general
design also, and the reader should refer to actual cars for
examples of the construction followed. When a three-point sus-
pension is obtained the front end is generally hinged or pivoted
so as to allow a certain freedom of movement, but at the rear
end, and at both ends with the two-girder type, the ends are
supported and riveted to either the front or rear main. cross
girder or a special girder between the side frames — the attach-
ment being either direct or through the medium of lugs or
brackets.

In both of these designs a thin metal plate may be fitted
between the frame and the engine which is conducive to cleanli-
ness and assists in giving that smart appearance which is so
much desired. Also, very short arms are necessary, which is an
excellent point in their favour, since they stiffen the crankcase
as a whole, and reduce to a large extent the reliance which must
otherwise be placed on the aluminium.

ThiBre are modifications of these methods in which either the
gearbox or the engine is carried on a separate underframe or

230 MOTOR CAE ENGINEERING

cross-frames, or the former is slung from the side frames by
means of brackets, lugs or clips, but, except that so great reliance
upon aluminium is not necessary, it is difficult to see >vhat
advantage accrues and it certainly adds to the weight and
complication.

With the last form (c) there are really two forms of this —
when the attachment is direct and when secured to a girder or a
bracket brought out from the main frame. Both forms are
adopted in current practice, and are subject to the defects that
any distortion of the framing is ultimately transmitted to the
crankcase and the gearbox and that the relative motion of the
two causes a considerable amount of work to be done by the uni-
versal joint in the clutch shaft. These remarks anent distortion
do not, of course, apply to those designs where a three-point
suspension is given to the crankcase or to the gearbox, as the
advantages derived then still obtain, except as regards the rela-
tive movement between engine and gearbox, which is taken up
by the universal joints. There may be four or six arms to the
crankcase (depending upon the size of the engine) and generally
four arms to the gearbox, or there may be a flat plate extending
the whole length of the engine or the gearbox which is bolted to
the frame. The latter cannot be considered a good construction
in one sense since apart from any question of distortion it pre-
vents the freedom of access to parts below the framing and
obscures the light, yet at the same time it is beneficial in that
it causes most engine parts to which immediate attention is
occasionally necessary, such as the carburetter, magneto, water
pump, etc., to be placed in an excellent position.

It will be clear that where an underframe of any kind is
employed the question of the extra weight involved must receive
consideration — and is a very important matter in large engines,
especially when both engine and gearbox are suspended on the
same underframe.

CHAPTER XII

ENGIKE LUBRICATING AND COOLING ARRANGEMENTS, INLET, EXHAUST

AND FUEL PIPING, ETC.

131. Lubricating ArrangementB. — Several systems of engine
lubrication have been discussed and illustrated in Vol. I., Arts.
282 to 240, so it will be unnecessary to do more than summarise
and amplify the remarks there made. The need of an effective
system hardly needs emphasis after one has seen a car moving
through traffic leaving a dense cloud of smoke behind, and the
condition of the cylinder under such circumstances can be better
imagined than described.

The splash system is the oldest and the simplest, but is seldom
used in modern cars because of the difficulty of maintaining a
uniform supply to the cylinders and bearings by reason of the
fluctuating level in the crankcase with varying speeds, with the
inclination of the car and as the oil is consumed. For this reason
the system is wasteful, and since the burnt oil and carbon from
the cylinders fall back into the c):ankcase, it is extremely probable
that the lubrication will be less satisfactory and result in wear
and be more liable to failure due to the stopping up of the lubri-
cating holes at the bearings. The effect of inclination is mini-
mised but not entirely eliminated by the use of division plates in
the crankcase, while the quantity of oil available may be main-
tained if the makeup is from continuous supply from, say, a
tank which delivers oil to a drip feed (a device that requires
continual attention), placed on the dashboard, but there are many
possible modifications. The supply may be led direct to the
crankcase or to the main bearings, or to the cylinders and the
bearings. Continuous supply to the dashboard tank can be
ensured, either by exhaust pressure, or by air pressure from a hand
pump, or the oil contained in a reservoir which is frequently
placed under the bonnet, or the main supply may be from a dash-
board tank, or mechanically by the use of a small pump driven by
the engine. Intermittent supply to the crankcase is obtained by

232 MOTOR CAR ENGINEERING

pumpiDg a quantity of oil from a dashboard tank by hand at
such intervals as the experience of the driver dictates. Such a
system is however irregular and is not compensated for vary-
ing engine speed ; therefore the lubrication is at times slightly
below and at others slightly above the desired quantity,
besides which, it diverts the attention of the driver to some
extent.

The trough system, which is a refined or improved splash
system, has been adopted by many manufacturers, because, it is
said that while affording effective lubrication, it is slightly cheaper
and more simple. But it is extremely doubtful whether these
claims can be substantiated in every case. If the trough system
simply consists of narrow troughs placed beneath each connect-
ing rod end, with overflows from each trough to regulate the
depth to which the dippers are immersed, then its cheapness and
simplicity must be accepted. But with the arrangements usually
employed there is a combination of forced system to the main
bearings and the trough system to the crankpins and gudgeons,
while occasionally the level of the troughs is under control,
being interconnected with the throttle so that the depth of im-
mersion of the dippers varies with the power developed. Hence,
any comparison must be made between two particular systems
rather than two general forms, and in many cases the forced system
is the superior in these respects'. This also applies to the claim
sometimes made that the trough system is more economical, as,
when effectively carried out, the forced system can be made
to be most economical in consumption. Difficulties often arise
in practice with a forced system apart from those associated
with the design, because of the excessive clearances allowed,
since it is essential that these are as small as possible for
successful operation, so that the excessive flow of oil from
the bearings which is splashed in the crankcase and on to
the cylinder walls may be prevented, while at the same time
sufficient oil is carried through the system to effectively lubricate
the crank and gudgeon pins.

Not infrequently the leakage of oil from the main bearings
(where it is introduced under pressure) is relied upon to lubricate
the crank and gudgeon pins, and pistons and baffle plates or
'' guides " are fitted to divert the oil to the former, the latter
being lubricated by splash. But the fully forced system is

ENGINE LUBRICATING AND COOLING, ETC. 233

admirable — clean oil in a sufficient quantity is supplied to every
part, friction is minimised, wear is reduced, reliability is increased
and a more silent operation ensured. The disadvantages of com-
plications, and the reliance which must be placed upon the pump,
can hardly be considered as of sufficient importance to detract
from the otherwise excellent qualities, and further, they are
present in the trough system, while the dependence of the main-
tenance of the efficiency of the system upon the condition of the
bearings is of little consequence, because if properly fitted in the
first instance they are subject to extraordinarily little wear.

132. It is essential whenever a pump feed under pressure is
employed to use a substantial construction, since the supply of oil
oil is entirely dependent upon the completeness of the system.
For this reason, steel pipes should be fitted where the oil ducts are
not taken through the crankcase casting, and all passages should
be of large area, since with the low temperatures that often obtain
more damage can be done during the first five minutes, when the
oil supply is limited owing to its high viscosity, than during a
week's ordinary usage ; further stoppage by impurities is ren-
dered more remote. Too great reliance must not be made upon
the gauge or the tell-tale generally fitted on the dashboard,
because the driver*s attention is usually directed to other matters
and failure may occur any instant. It would seem to be an
advantage to fit an oil reservoir in the crankcase, or what would
serve a similar purpose, to use large bore pipes, so as to prolong
the time between which lubrication ceases and failure occurs.

The pressure at which the oil is fed to the bearings is not of
great importance provided, that it is fed continuously and in
ample quantity, although this may be qualified by saying that
the greater the pressure employed the higher the load the bear-
ing will carry without abrasion. And again, a high pressure
necessitates a large pump (partly because of the greater slip),
therefore the greater quantity of oil passing through the system
will assist in keeping down the temperature as well as ensuring a
maintenance of fiuid friction only.

Probably the greater difficulty still met with in modern work
is that of keeping the cylinders from being over-lubricated and
the bearings lubricated. Baffle plates, sometimes separate from,
at others cast with, the cylinders, are fitted at the bottom of the
cylinders with slots cut in the centre through which the connecting

234 MOTOR CAR ENGINEERING

rods operate. This, however, is not altogether satisfactory since,
with the exception of fully forced lubrication engines, the air
within the crank-chamber is charged with a spray of oil, and on
the upstroke of the piston this is drawn into the cylinder, drench-
ing the cylinder walls as well as lubricating the gudgeon-pin.
The supposition that oil splashed on to the piston dropped on to
the gudgeon-pin is now no longer considered as true. There are
several ways of overcoming the excessive lubrication of the piston
and the entrance of oil into the cylinder. In the first method, a
scraper ring is employed on the piston, and in the second, holes
are drilled through the skirt which besides reducing the weight
enable the oil which works up between the piston and the cylinder
to be squeezed out. • In the third method baffle plate is inter-
posed above the crank and extends the full length and width of
the crank-chamber, so that the air drawn into the cylinder with the
piston on its upstroke comes largely from that being expelled
from another cylinder and is therefore less highly charged with
oil.

In arranging for a lubricating system, where a pump is employed,
there are several points that must receive attention, one of which
has already been mentioned, namely, the use of steel pipes of

large bore. Mr. Morcom suggests that the delivery pipes should

/p ^ ^ /p

have a bore of ^- - and the suction pipes of ^^^ where P is the

19'4 ^ ^ 17'7

sum of the peripheries of all bearings at the discharge point, the

bore being greater for suction pipes so as to avoid a restricted

suction. These rules will give larger pipes than are commonly

used, but are certainly such as to merit attention. The leads to

the bearings will naturally be of reduced bore. There should be

a filter provided of large area, which must be detachable for

cleaning purposes, and should be arranged so that it is possible

to remove it readily and without losing the oil in the crankcase.

To enable this to be done, the filter is sometimes embodied in an

oil tank on the dashboard, from whence the fresh oil is drawn by

the pump and returned through the filter by a pump incorporated

in the same casting as the main pump. But this is quite

unnecessary and the separate tank is not altogether a desirable

fitting, while there are so many possible arrangements by means

of which the desired end can be attained — one being to place

the filter well up in the system, and another to bring a sump out

ENGINE LUBRICATING AND COOLING, ETC. 236

oil one side and arrange for the filter to be withdrawn upwards.
The piping should be as short aa possible without undue cramp-
ing and should be joined up by means ol union nuts, and where
braDches are taken off T or Y pieces should be inserted in prefer-
ence to brazing. A relief valve should be fitted on the delivery
side of the pump set to blow off at the desired pressure, the return
being taken, preferably, to the pipe lead on the pump side of the
filter, since the entrance of this oil under pressure into the oil
remaining in the sump would have the tendency to stir up any
sediment that may have been deposited there.

Fio. 34. — Wolseley combined air and oil pump.

188. Oil Pumps. — The pump fitted should be of ample capacity
for the purpose for which it is intended, as at low speeds of
rotation the quantity discharged may be comparatively small, even
though the loads are just as great as at higher speeds, while any
excess at high speeds is simply returned and not wasted, and it
may be added that the power required to operate the pump is
exceedingly small. There are three kinds of pumps in common
use — the plunger, the gear, and the shutter or vane pump. The
two first mentioned are the most important, as the latter is
rather simply for the purpose of feeding the oil to the bearings
and wilt not work against great pressure. It should be remembered

236 MOTOR CAR ENGINEERING

that the pressure at the pump (that is, the pressure at which the
system works) is that which is required to force the oil against
the various resistances. If the clearances are extremely small,
and sharp bends and long leads are avoided, the pressure at the
bearings will be high, even ' though only a small pump is fitted,
although this will be modified according to the centrifugal and
inertia effects on the oil in the system. The actual size of pump
must be based upon the practice at any particular works, since
the clearances allowed are not universally the same ; but Mr. Morcom
suggests^ the following rule for plunder pumps which is empiric in
its character —

Volume swept out by the pump on the discharge stroke per
minute = 8 P where P is the sum of the peripheries of all bear--
ings at each discharge point. This will be found to accord very
closely with general practice. Using this same expression for a
gear pump, the volume theoretically discharged by it should be
8 P, assuming that it has the same efficiency as a plunger pump
when new. The volume in cubic inches theoretically discharged
per revolution of the pump shaft is —

2 (ttR* — cross sectional area of the boss and the teeth) X I where
R is the radius to which the pump case is turned and I is the
width of the wheel, both dimensions in inches — Or, it equals —

2n (Area of the space between any two adjacent teeth and the

pump case) I
where ii is the number of teeth in one wheel.

Multiply either of these by N (the number of revolutions of
pump per minute) and the discharge per minute is obtained.
But whereas the plunger pump is positive and maintains its volu-
metric efficiency so long as the valves are in good condition the
gearwheel pump decreases in volumetric efficiency as time goes
on and wear takes place, thereby permitting the oil to pass back
to the suction side of the pump. The capacity of this pump
should therefore be made about 20 or 25 per cent, greater than
that of plunger pumps for the same work.

Hence —
2'5«ZN (Area of space between any two adjacent teeth and the

pump case = 8 P).

It is very essential for the efficient operation of the pump that
the wheels are a good fit in the casing, not only at the points of

1 Sec PivaedhigH of I.A.E., Vol. IV.

ENGINE LUBRICATING AND COOLING, ETC. 287

the teeth hut also at the sides, and further, that it is far more
satisfactory to use properly cut wheels because of the importance
of good contact of the teeth for a high volumetric efficiency. It
may be noted that with the plunger pump an engine should be
run for a short time under light load in order to heat up the oil
and reduce its velocity so that it may pass freely through the
valves.

The pump should preferably be " drowned '* as troubles
experienced in priming at starting are thus avoided, and this is
easily arranged for if the pump is driven by skew gearing from
the camshaft. In this position, the driving connection must be
of the dog type (Fig. 174, Vol. I.) and permit of axial movement
because the pump will be arranged in the bottom half and the
camshaft in the top half of the crankcase. If driven ofif the end
of the camshaft or in any other position where the oil has not a
free flow down to it, a priming cock is essential.

134. General Remarks. — The oil holes in the shafts must be
of ample area as there is no purpose in cutting down the dimen-
sions, and where they open on to a surface the edge should be well
rounded off. In no case should they be less than ^\^ in. (2*4 mm.)
for radial holes and 4 in. (6 mm.) for axial holes. To ensure the
supply of lubricant to the centre of the shaft, an annular groove
may be cut in the bearing and so arranged that the recess in the
upper half is not in the same transverse plane as that in the
bottom half, the two recesses being connected at the joint. The
oil grooves in the bearing for the distribution of oil over the
surface vary, but the general idea should be to take the oil
in at the point of low pressure and lead the grooves so that the
movement of the shaft draws the oil into the region of greater
pressure.

A lead will probably be necessary for the lubricating of the
timing gears, A^^d if the camshaft runs in a separate trough, for
the replenishment of this also. A tell-tale or a gauge will com-
municate with the system close up to the pump on the discharge
side and be fitted to the dashboard, while the level of oil in the
sump should be indicated by some means. Floats and similar
devices are troublesome, so that either a gauge-glass or a cock
must be fitted, the latter being preferred because generally the
former gets so discoloured as to render it impossible to see the
level or else is in such an awkwiard position for inspection in the

238 MOTOR CAR ENGINEERING

undershield that one cannot easily examine it. A cock is, how-
ever, dirty but sure.

There are many systems in. practice which, while coming
under one or other forms of lubrication, yet differ so greatly in
the mode of application. For an examination of these, the
reader may best refer to the Technical Press (articles have
appeared in the Autocar , AutomotoVy and the Autoviobile Engineer
from time to time) ; also to Mr. Morcom's paper above mentioned,
and to Arts. 232 to 241, Figs. 167 to 173, Vol. I., and Figs. 4,
5, 7 and 9, of this volume.

The lubrication of the chassis will be treated in conjunction
with the design of the part.

136. Engine Cooling. — Just as the engine lubrication is of the
first importance, so also is engine cooling, for they are inter-
dependent, because cooling is largely required in order to allow
of effective lubrication ; it is also necessary for structural reasons
and in order that a full charp:e of gas may be drawn into the
cylinders. In Chapter XIII., Vol. I., this question is discussed at
length, from a descriptive and comparative aspect, so it now
remains to consider the matter from the point of view of design.

136. Air Cooling. — The use of air coolinj? has, so far, been
restricted to motor cycles, aeronautical engines and a few light
low-powered cars, although some air-cooled medium-powered
engines have been employed in America. This has been possible
because of the peculiar position and conditions under which
cycles and aeroplanes are used and it is unlikely that their
extensive use on motor cars in this country can ever become
possible, because speeds are not sufficiently high, neither are the
engines sufficiently exposed to enable efficient cooling to result.
Auxiliary exhaust ports assist in getting rid of the exhaust gases
and thus conduce to a lower cylinder temperature, but these
must be enclosed or else an unsightly engine results, and even
then the results obtained are not equal to those from water-
cooled engines. Attempts have been made to render. such an
engine successful by using a fan placed within a casing which
surrounds the cylinder, but the complication, weight, expense,
and the power required to rotate the fan more than counter-
balance any advantages that may accrue, and unquestionably
water cooling is the more efficient system.

In arranging an engine for air cooling it is essential that the

ENGINE LUBRICATING AND COOLING, ETC. 239

fins are so placed that the natural flow of the air is along and
between them, for it is only by so doing that the fullest advantage
is taken of the velocity of the air, and as air has a very low con-
ductivity it must come into direct contact for efficient cooling.
Fins will therefore be arranged in the direction of motion. When
it is necessary to place a boss upon the cylinder, it should be
put as far back as possible so as to reduce the disturbance
of the air to the greatest extent. The thickness of the fins
should be about -^^ in. (5 mm.) at the junction with the
cylinder, and' have a good radius, tapering ofi" to about ^\ in.
(2'5 mm., at the extremities. This tapering of the fins assists
in reducing weight and facilitates casting ; while uniform thick-
ness is not necessary since the heat is carried away from the
whole surface of the fin. The width of the fin should be about
f in. (18*5 mm.).

Dull black surfaces are the best radiators, so the cylinder and
fins should present such surfaces.

137, Water Cooling. — This is the method most commonly
employed for car engines, and as applied may be worked either
by thermo-syphon or by forced circulation, but in any case the
flow of water should be such as is traversed by the natural
circulation of water, that is, it should be taken in at the point
of lowest temperature and pass out at the point of highest
temperature.

With thermo-syphon the passages through the cylinder
casting should be quite clear and the pipes of largo diameter, not
less than 1 J in. (32 mm.) bore — and there should be an absence
of pockets or downward bends in which air or steam can collect.
It must not be forgotten that water absorbs a quantity of air,
which, when the system is heated up, is liberated and may
collect in some part and form a " lock " thereby stopping the
circulation and causing local overheating. Such a lock is not
easy to remove, as the steam generated only tends to aggravate
the trouble. The outlets should therefore always have an
upward trend and are sometimes arranged so that they cover the
entire cylinder head. For a forced system the pipes may be
about I in. (18 mm.) diameter or even smaller since natural
circulation is assisted by the pump. With pair block cylinder
castings the inlet and outlet should be so placed that the water
is free to pass equally round each cylinder, and this applies to

240 MOTOR OAR ENGINEERING

four-cylinder castings in that two inlet pipes should be fitted
with their orifices between the two front and the two rear
cylinders.

The piping communicaling with the radiator and pump should
always be connected by rubber tubing secured by ^lips, because
vibration and expansion cause trouble where union nuts or any
rigid connection is employed. All branches from the pipes and
all leads taken ofif for such purposes as heating the carburetter
or dividing the leads to the cylinder should be arranged so that
the flow of water is continuous, for which reason Y pieces should
be inserted as necessary. Oast pieces at the junctions of branches
and pipes are preferred although they prove more expensive to
manufacture, but ultimately save money and trouble.

A drain cock should be provided at the lowest portion of the
system — frequently at the bottom of the radiator or oflF the pump
casing, whichever is tlie lower — so that in cold weather, and when
the engine is being overhauled the jackets, piping and radiator
may be emptied without inconvenience.

The pump, if fitted will be located in the pipe between the
lower part of the radiator and the cylinder and will drive the
water through the cylinder casting.

188. Water Pmnps.— At the present day there are two forms
of pump in common use — the centrifugal and the gear pump,
the former being preferred because in the event of the pump
failing thermo-syphon action is at once instituted, and further,
gear pumps are subject to wear at the teeth, in which event their
capacity is reduced. Shutter pumps are also occasionally
employed, but they are subject to excessive wear at the blades
and the case.

The function of the pump is not to pass a definite quantity of
water in a given time, but to force the water through the jackets,
thus assisting the natural circulation although incidentally it
does do so. The quantity of water in the radiator, piping, and
jackets, and the speed at which the water passes through the
system have little practical effect upon the limits of working
temperatures — the former because whatever the quantity used it
would soon be heated up if the cooling apparatus is insufficient
although the greater the quantity of water the longer the time
before which boiling water would take place, hence a car used in a
hilly district or in town should have a large water capacity ; and

ENGINE LUBRICATING AND COOLING, ETC. 241

the latter, because if the velocity of the water is increased, the
time in contact with the cylinder walls for Ihe reception of heat
is less and the time passing through the radiator for coohug also.
Hence, the size of the pump must be left to the judgment of the
designer, who will have regard to the space at hia disposal and
the convenience of his arrangement.

It will be generally found that 3 in. (75 mm.) is the smallest
diameter that can be given to the impeller of a centrifugal pump.

Pio. 35. — Woleeley Centrifugal Pump.

while the dimension seldom exceeds 4| in. (120 mm.). Pro-
bably the greatest drawback to this class of pump is the side-
thrust on the bearings from the pressure at which the water is
discharged. To overcome this, two outlets have been fitted — one
diametrically opposite the other ^ — but in any case long bearings
are essential for its extended use, and to limit the possibility of
trouble from leakage of water on the one hand, and the entrance
of grease or oil into the water system on the other. The pump
cases may be made either of aluminium or of gunmetal, and if of

242 MOTOR CAR ENGINEERING

the former, sliould be bushed at the bearings ; with the latter, it
is really optional, although desirable. The impeller may be of
either of these metals, but in any case must be well secured and
be true with the shaft. The shape of the impeller blades seems
to have little effect ob the satisfactory operation of the pump,
probably owing to the factors mentioned in the preceding para-
graph, and to the variation in the speed at which the engine runs.
For the highest efficiency at any particular speed the blades should
have such a curvature that a particle of water in moving radially
outwards under centritogal force
would trace out such a curve on
the impeller as it rotates — the curve
therefore represenfs the relative
motion of the water to a radial
line on the impeller. Steel shafts
are often used, but manganese
bronze is more suitable for the
purpose on account of its non-cor-
rosive properties, and has the
additional merit that the impeller
and the shaft may be cast and
machined in one piece. The shaft
j'lo ae will be from | in. to ^ in. (16 mm.

to 19 mm.) in diameter and should
preferably be run at a speed not less than that of the engine.
Not infrequently it is driven on the same shaft as that for the
magneto, for four- and six-cylinder engines.

Gear-pumps should be made entirely of good hard bronze, with
similar pumps used for lubricating purposes the wheels may be
of steel, but for water pumps some non-corrosive metal is
imperative because of the medium in which they work. The
provision of long bearings is not so essential, although it is
desirable, as in centrifugal pumps, since both bearings for one
wheel and one bearing on the driving wheel are entirely enclosed
and the remaining bearing is provided with a gland to prevent
leakage. ' But good bearing surfaces are necessary, especially at
the gland, for long and efficient operation, since much depends
upon the absence of clearance and wear round the teeth and at
the sides of the wheels. Grooves cut along the tops of the teeth
and down the ends asaist greatly in preventing, the water from

ENGINE LUBRICATING AND COOLING, ETC. 243

slipping past at these points, which would diminish the efficiency
of the pump, that seldom exceeds 70 per cent. Bushes of a softer
grade of metal should be fitted at the bearings, as by careful
attention to these the durability is increased. Makers often
prefer the use of a fairly large size of tooth because by this
means a relatively greater capacity is obtained for any given
overall dimensions of the wheels, but with a small number
of teeth the points of contact are few, and, therefore, there is a
greater liability of leakage. Attention is drawn to the method
of attachment of the driving spindle at the wheel and at the
driving end, for not infrequently it is found that the. diameter at
the gland is no larger than at some other part in the length of
the spindle,' so that its removal is difficult, and when wear takes
place the renewal of the shaft is necessary. The gland should
be locked against movement by some means — either by a set
screw (which should be kept clear of the thread), or by the use
of a spring clip. The details, driving gear and attachment to
crankcase will largely depend upon the particular construction
employed, and are, therefore, not dealt with here,

139. Eadiators. — Radiators are generally of one of three forms,
the gilled tube, the honeycomb, and the plain tube. (See Art. 162,
Vol. I.) The thickness of the tubes varies slightly, but this is only
of importance from the question of weight and cost of material
owing to the relatively low conductivity of the air.

It has been stated that an engine will be most efficient and give
out its maximum power at a certain temperature of the cooling
water, but it will be manifest that this is of little consequence
when considering engines for car purposes, since the conditions of
power, wind, speed, atmospheric temperature and even of the
heat loss to the cooling water are so variable that estimates of
temperature are of little value.

The heat loss to the cooling water at full power per minute is
from 30 to 40 per cent, of the heat of the petrol. Assuming that
it is 85 per cent, and that the thermal efficiency is 24 per cent,
(it may reach 28 per cent, under ideal conditions), then for

every indicated horse-power developed ^-r = 1*46 H.P. are lost to

cooling water, which are equivalent to ==j = bJ a

B. T. U.'s per minute. If the radiator reduces the temperature of the

R 2

244 MOTOR CAR ENGINEERING

waterby 50 degrees in passing (apurelyarbitrary value), the weight

62 '2
of water required to pass will be -ttt = 1*244 lbs, per H.P. per

minute. The drop in temperature will depend principally upon —
(a) Total cooling surface in the radiator.
{b) Nature and condition of those surfaces.

(d) Velocity and quantity of air throu^gh the radiator.
{e) Temperatures of the air and the water.

The factors (a) and (b) may be regarded as permanent, but not
so the others, as the speed of the engine and the car varies con-
siderably ; the direction of the wind is sometimes with the. car,
at others against it; changes take place in the atmospheric
temperature and in the power developed, etc. Hence, even if the
heat radiated per square foot per degree difference in tempera-
ture on the two sides of the pipe is ascertained for any given
radiator, it is of little service except for a comparison between
the efficiencies of any two radiators.

For plain copper tubes there should be between 1*5 and 2*5
sq. ft. of surface per B.H.P., for a honeycomb radiator about
3 sq. ft. per B.H.P., and for gilled tube about 5 sq. ft. per B.H.P.
The low proportion for plain copper tube is probably explained
by the fact that the air has freer access to the tubes than with
either of the others, while the honeycomb radiator is perhaps
more efficient than the gilled tube because the gills are attached
to the tubes by a solder that has a lower conductivity than that
of the tube and because the water is not in close contact with
the gills. The ratio of gill surface to tube surface is generally
from about 6 to 1 to about 8 to 1 and depends somewhat upon the
size of the tube and whether the gills are circular or square with
rounded corners. The gills are generally crinkled and pitched
about J in. (6 mm.) apart — if closer than this the passage of the
air between them is somewhat restricted. The length of the
honeycomb tube should not exceed 5 in. (125 mm.), otherwise the
friction of air along the tubes increases sufficiently to reduce the
capacity of the radiator. It will be found to be necessary to cat
down these proportions for higher power cars ; but this is not of
importance, since the engines seldom develop their full power,
except at high speeds, when lower values are permissible because
of the higher cooling efficiency of the radiator. For fans see

ENGINE LUBRICATING AND COOLING, ETC. 246

Vol. I., Art. 164. They may be mounted on either ball or plain
bearings supported by the front cylinder, the crankcase or the
radiator, but the latter is not deemed advisable, as it may cause
sufficient vibration, in the event of the fan being out of balance
either due to bad manufacture or from a blow, to cause a leaky
tube. Every precaution should be taken to render the radiator
immune from strain of any kind by mounting it upon pivots
or rollers, or some substance such as felt or rubber that will
absorb a certain amount of shock. It may advantageously be
mounted on trunnions lined with rubber, as is often done, light
stays being fitted to restrict the movement of the top of the
radiator and prevent the disturbance of the pipe connections.

140. Inlet and Exhaust Piping. — From the many shapes given
to the induction pipes it will be clear to the careful observer that
there is no one set way in which to arrange them, but there are
several rules that should be observed if an equal charge is to
be drawn into all cylinders. The first is that the volume of the
piping between the inlet valve and the carburetter should be the
same, that is, each cylinder should draw from the same volume
of piping. . There are fluctuations in pressure in the inlet pipes,
and unless this rule is followed there will be a perceptible lag in
one or more cylinders that will affect the charge taken by them.
As far as possible, also, the shape of the piping should be similar,
so that the fall of pressure along the pipe due to the various
bends, contractions, etc., may be uniform. Cast Y pieces may
be used where the pipes branch, and all bends should have a good
curvature so as to prevent the reductions of pressure being
excessive, or the petrol, which is then in a state of suspension,
from being deposited through striking a cold surface.

All joints should be carefully attended to in order that there
may be no possibility of leakage of air, which is so disastrous to
efficient carburation when running under light load with closed
throttle. Some makers believe in surface joints, but whatever
form of joint is employed it is desirable to use spigots. The
drilling of holes in the inlet pipes to supply a little air to one
cylinder is a practice that should be strongly deprecated.

So far as arrangements are concerned, in many pair cylinder
castings the carburetter is placed on the offside of the engine
and branched to each pair of cylinders, the lead to both inlet
valves being taken through the casting itself, as seen in Fig. 5 ;

246 MOTOR CAR ENGINEERING

while in others this lead is a separate pipe between the cylinders
and outside the easting. In some cases Nos. 1 and 2 are coupled
together, and Nos. 8 and 4, and these pipes fed by a connecting
pipe attached to their centres which is served by a short lead
from the carburetter. In one instance, a tapered pipe is used,
but the actual leads are very varied and should be studied on the
engines themselves, because the number of cylinders and the
method of casting affect the arrangements employed so greatly.

Aluminium, copper and gunmetal are all used in the manu-
facture of these pipes.

The exhaust pipe usually has a separate lead from each
cylinder ; and the remarks as to bends and Y branches apply
here with equal force, for the reason that sharp changes in the
direction of the flow of the gases cause an increase in the back
pressure, and the impinging gases overheat the piping. In order
to provide free access to valve tappets and springs, etc., the pipe
should be kept well up on the engine until it nears the dash,
when it should take a good curve downwards till the footboards
are reached and then curve to the rear as gradually as possible.
The branches should enter the exhaust manifold at an angle so
that the direction of the gases is to the rear ; and if two cylinders
are exhausting at the same time, as in four- and six-cylinder
engines, the provision of a nozzle in the interior of the pipe is an
advantage, since the exhaust froin the front cylinder as it rushes
past that nearest the rear exercises an ejector action, preventing
the exhaust from returning to a cylinder in front, as might happen
say in a four-cylinder engine when No. 3 opens to ftxhaust and
No. 1 is just finishing the expulsion of the gases. Where this is
not provided, a small lip, cast in the pipe, may be used.

The material used may be either malleable cast or ordinary
cast-iron of about Jin. (3*5 mm.) thickness. The cross sectional
area of the pipe should be made to be about twice that of the area
through the exhaust valve.

Connections may be necessary for either the heating of the
carburetter, for supplying pressure to the petrol tank, or for
pressure to an oil tank, and should be arranged for by casting
pads of suitable shape upon the pipe. It is always advisable to
do this, even though pressure feed is not contemplated, as it
renders the fitting of such a system subsequently much more
satisfactory.

ENGINE LUBRICATING AND COOLING, ETC. 247

141. Fuel System. — The main points to be borne in mind here
are that the pipes should be of ample bore, that in no case should
the pipe bend downwards, and that a filter with an upward flow
is imperative. The reason why a small pipe is objectionable is
obvious, and when a very tortuous lead is given an apparently
large enough pipe often is too small, especially where the filter
has not received attention. Downward bends should be avoided
because impurities sink to the bottom and may choke the pipe,
while the filter does not always remove all foreign matter. The
filter is required to prevent, so far as practicable, any dirt from
entering the piping and should be placed in an accessible position
near to the tank. A cock should be fitted close to the tank before
the filter, and preferably also between the filter and the engine, as
this latter can generally be arranged in a convenient position
for shutting oflf the petrol when stopped. The former is necessary
to enable one to clean the filter without losing petrol, and is
usually on the tank itself under the floorboard. The filling hole
to the petrol tank should be of large area, and a small hole should
be drilled through the cap to admit of air entering as the petrol is
used unless pressure feed to the carburetter is fitted.

If pressure feed is used it is necessary to filter the gases when
exhaust is employed for creating pressure, and a relief valve is
essential. This pipe is taken to the top of the tank, but that
supplying petrol to the carburetter should be taken to nearly the
bottom. A drain cock can be fitted at the bottom with
advantage.

It is hardly necessary to add that all joints should be made
with coned union nuts and nipples and reduced to the minimum
number that it is possible to use.

For remarks on control systems see Chapter XII., Vol. I., but
the necessity of the employment of the simplest and straightest
lead, and the elimination of ballcrank and other levers, with
their multiplicity of working joints at which wear can take place,
is strongly emphasised. See also the Automobile Engineer for
June, 1912.

CHAPTER XIII

CLUTCHES AND BRAKES

142. Clutches are required in order to rapidly and easily
disconnect the road wheels from the engine in cases of emergency
and when changing gears. Under normal running conditions
two or more surfaces are held in contact by a spring or springs
which may act directly on the moving member or through the
medium of levers. Any great amount of slipping is to be
deprecated, although some forms of clutch will permit of this
being done to a reasonable extent without any harmful efifects
arising. Disengagement is effected by a pedal which is operated
by the foot. Brakes are fitted in order to arrest the motion of
the vehicle quickly, quietly, and smoothly, and effect their pur-
pose by converting the kinetic energy stored up in the moving
car into heat at the brake drums which is dissipated, more or
less effectively, by radiation into the atmosphere and by con-
duction to the parts to which the drums and shoes are attached.
In this case, however, slipping is imperative if the manner in
which the car is brought to rest is to be as indicated above.
The actuating mechanism is controlled by hand and foot levers
which operate the shoes through rods or wires and levers, but
springs are fitted to disengage the shoes as and when required.

For descriptive matter relating to clutches and brakes the
reader is referred to Vol. I., Chapter XV.

143. The Design of a Clutch. — It has been stated in Vol. I. that
a clutch should be free from complicated parts that may require
frequent adjustment and that are not easily dismantled or
assembled, for, as in every other part in the car, the great aim
should be to obtain simplicity. Clutches should also be self-
aligning and self-contained, the former in order that the
relative positions of the acting surfaces may be correctly main-
tained under all conditions, and the latter so that the pressure
of the spring may not be taken up by any extraneous part or
thrust the crankshaft in either direction when the clutch is in

CLUTCHES AND BRAKES 249

engagement. The inertia of the rotating parts attached to the
dutch shaft should be low, otherwise they will take a prolonged
time to slow down when changing gears and probably cause con-
siderable noise when the gears are meshed, as the wheel teeth
have seldom exactly the same linear velocity when brought into
engagement. To enable the drive to be gradually taken up, a
certain amount of slipping is desirable and necessary, although
the extended slipping of any clutch is to be strongly deprecated,
since it has the effect of raising the temperature of the parts,
causes undue wear, and in many cases produces a very fierce
action. Lastly, when the clutch pedal is depressed, the clutch
shaft must be completely disconnected from the engine. It must
be acknowledged that in some cars this is not so, with the
inevitable result that the operation of meshing the gears, say, at
starting necessitates the use of considerable force and may cause
noise and shock.

The design of a clutch is in three parts, namely, the frictional
surface required to transmit the torque, the arrangement and
construction of the details, and the strength of the springs, levers,
etc.

As regards the first part, the methods of design will be similar
for single cone and double cone clutches, for plate and expanding
clutches and multiple disc clutches stand alone — these will be
examined shortly. The work involved in the second division is
one that must be carried out entirely by the designer, and the
reader may either refer to Figs. 37 — 41 and to Vol. I. or to the
technical press for contemporary examples, but he should
endeavour to exercise his originality in devising some new
design. The design of the springs and levers is the same in
almost all clutches and will be considered in Art. 147.

144. Ctone Clntclies. — This form of clutch is that which is most
extensively used, mainly on account of its simplicity, cheapness
and the ease with which renewals can be effected ; but, unless
the engine runs at high speed, the provision of ample frictional
surfaces that will withstand wear and give a smooth action over
long periods with high powers presents considerable difficulty.
Increase in diameter or width of surface assist in overcoming
this but are accompanied by increase in weight at the rim,
the part in which extreme lightness is essential; hence the
intensity of pressure is sometimes increased beyond that which

250 MOTOR CAR ENGINEERING

is desirable, since eome measure of durability must needs be
sacrificed.

The material need for tbe male surface of the clutch is either
leather or raybestos — usually the former (although metal sur-

FiG. 37.— 12-16 h.-p. Wolseley Clutch.

faces have been employed) — and these are secured either by
riveting or by means of bolts. The latter is preferred, and is
more generally fitted because of the facility with which renewals
may be effected. The inner portion may be made of pressed
steel, cast steel, or aluminium, but if the latter is used it should
be well supported at the centre by a steel plate or attached to
a steel boss. To facilitate smooth engagement, flat or helical

CLUTCHES AND BRAKES 251

springs are sometimes placed beneath the leather, so that when
the drive is taken up the leather lies flat upon the surface of
the clutch.

The torque is transmitted by the frictional resistances to
relative motion between the acting surfaces. These surfaces are
pressed together by a force P, then if the radius to the centre
of area is r and the coefficient of friction is /x, the torque
transmitted is Pfxr lbs. in., or kilos mm., according as the
units employed are English or metric. Hence, if the maximum
twisting moment is T^ —

T,, = Ffir.

It is usual to take r as the mean of the two radii of the
ends of the cone, although this is, strictly speaking, incorrect,
but the error involved is negligible.
No\v P = 2Trrwp (nearly)
where w = the width of the surface along the cone

p = the permissible unit intensity of prepsure.

Therefore T,^ = 2TT)^fjLtcp.

For leather and cast-iron fi = 0*25 and ;> is not more than
5 lbs. per square inch or 0*0035 kilo per mm.^

Hence

T,^ = 7'85i^w lbs. in.

= 0*005 )^w kilos mm.,
from which r and ?/■ can be adjusted so that the surface will
transmit the required twisting moment.

For double cone clutches T,^ will be divided by 2 to obtain
the twisting moment transmitted by each portion, and the pro-
cedure will then be as has been indicated above. When both
surfaces are of cast-iron, as in some metal to metal clutches,
fi may be taken as 0*175, and if one is of gunmetal and the
other of cast-iron u = 0*2. The permissible pressure per square
inch is from 80 to 40 lbs. or per mm.^ 0*021 to 0*028 kilo.

145. Multiple Disc GlntclieB. — The acting surfaces in this type
of clutch, with the exception of the Hele-Shaw, consist of a
number of flat plates divided into two sets, one set being
driven by the engine and the other carried by the clutch shaft.
(See Figs. 37 and 38.) The plates are arranged alternately one of
each set and are held together by an external spring — engagement
or declutching being effected in the usual manner. Flat
springs are sometimes provided for separating the plates, which

252 MOTOR CAR ENGINEERING

otherwise cling together and tend to keep the clutch shaft
rotating, and occasionally one set of discs is cut along a
radius for a short distance for a similar purpose. Some device
of this nature, although not always fitted, is none the less very
desirable. One set of plates is generally of phosphor hronze and
the other of steel of about No. 18 L. S. G.
The pressure forcing the plates together in this case is that

Flo. 38.— 15-9 Araistrong-"Whitworth Clutch.

exerted by the spring F and is applied to all the acting sur-
faces of the plates. Let n be the number of acting surfaces, and
r the radius of gyration of the internal (ri) and external (Ri)
radii of the acting surface, that is, Ri is the outside radius of the
inner set of plates and Vi is the inside radius of the outer set of

plates. It will be found sufficient to take r as equal to ■ ' „ - ^ ,

since it is unwise to make the breadth of the surface very
large — | in. (18 mm.) is ample. In some designs n will be
twice the number of plates on the driver, but in others twice the

CLUTCHES AND BKAKES 268

number of plalee minus 1, depending upon the design employed
and how the plates are supported and arranged.

Then

T„ = nYfir.

But F = ir(B; —ji)p, '

where p is the permieeible unit pressure.

Therefore T« = nn(R; — ii)pii.r.

The value of n will vary according to the ideaa of the
designer, ft may be taken as 0'08 and p as between 20 and 30 lbs.
per square inch or 0-014 and 0'021 kilos mm.*

Fio. 39— Argyle Plate Clutch.

Hence,

T„ = kn{V.l - r\}>;
where k is from S'O to 7'5 for English units and from 0'0035 to
0*00525 for metric units.

By selecting a probable number of plate surfaces, the value of
(KJ — r\)r is found from which the value of Ri and ci can be
calculated ; or, if desired, a width of plate surface and the pro-
bable value of r may be assumed and the number of plate
surfaces required found by substitntion.

146. Plate Clutches. — One form of these clutches is illustrated
in Fig. 40, and the Deasy clutch is seen in Fig. 112, Vol. I.,
from which it will be seen to differ from the preceding, in that
the number of discs is reduced to two, occasionally to one, and
that the force exerted by the spring is magnified by trans-
mission through a multiplying lever. These plates require to
be much stouter than those for disc clutches because they are
subjected to greater load.

The twisting moment is, as before,

T„ = m7i(E; — ii)pfir,
where Bi and f'l are the external and internal radii of the

254 MOTOR CAR ENGINEERING

surface in contact and the other letters hsrve their previous
significance, ft, may be taken as O'l (a higher coefficient of

friction is taken here heeause wear is more pronounced in plate
than in multiple disc clutches) ; p lies between 25 and 35 Ihs. per
square inch or 00175 and 0-0245 kilo mni.^

CLUTCHES AND BRAKES 255

Hence,

T, = kn(El - 7i)r,

where A: is from 7'8 to ll'O for English units and from 0*0055 to

0-0077 for metric units.

For expanding clutches similar data may be used, but the
surfaces in contact will be the area of the separate shoes.

147. Clutch Springs, Levers, etc. — The strength of spring for
multiple disc clutches is obtainable directly from pressure on the
surfaces and is —

Spring load = -nij&l — 1^)^,
the value of p being that which has been used in determining
the surface required.

For plate clutches^ the total pressure on the transmitting
surfaces is m times that exerted by the spring, because of the
multiplying efifect of the levers. Hence,

Spring load = -n ^ ^^ — ^,

where m is the ratio between the distance from the centre line

of the spring and the fulcrum and the distance from the centre of

the pin operating a presser and the fulcrum.

But with cone clutches the spring load is augmented by the
wedge action of the cone, so that further investigation is
necessary. The pressure on the clutch surface is from Art 144
= P = 27rncp.

Turning to Fig. 41, the diagram shows the forces acting,
F representing the spring load and P the total pressure on
the clutch surface. The force necessary to keep the surfaces
in contact with a total pressure P between the surfaces is
evidently P sin ^ ; but there is, in addition, the frictional resist-
ance to tlie movement of the male member into engagement
with the female portion, and this acts along the surface from
T to R, its magnitude being P/a. The resolved part of this
resistance in an axial direction, since RTS is equal to 0, is
Tfi cos 0,

Hence the total spring load is —

F = P (sin ^ + fx cos 0).

This additional load, P/a cos 0, is required because one surface
moves over the other before effective contact is made, but after
this takes place the acting force could be reduced without causing
the clutch to slip.

256

MOTOR CAR ENGINEERING

The value.of ^is always made to be approximately equal to
tan ~VI> because if is greater than this, the spring must be
made to give a greater axial load, and hence the force required to
operate the clutch is increased, while if smaller there is a proba-
bility of jambing. The coefficient of friction, /m, for leather or
metals may be taken, as before, to be 0*25, although it will be
quite obvious that it will depend upon the amount of oil present
on the surfaces. Then tan "^0*25 = 14° 2', but is generally made
15 degrees, as it gives an easy angle for working to and is permis-
sible because of the variation that fi may be subject to. For cast-
iron to cast-iron surfaces of the cone type, fi may be taken as 0*175,
and tan *"V then becomes 9° 56', say 10°, while if of cast-iron

and gunmetal ft = 0*2 and

^ r

Fig. 41. — Cone Clutch.

tan -y =11° 19', say,

iir.

Knowing 0, fi and P,
F can be calculated from
the above.

The proportions to be
given to the spring will
be somewhat dependent
upon the design of clutch.
In some cases a single spring is employed, but in others three or
more are used, in which case the total load F will be divided
between the three or more springs. There seems to be little
against the latter arrangement except that it is difficult to obtain
springs having exactly the same compression for any given load,
or that take the same permanent set after use, consequently the
distribution of the pressure is not equal over the whole surface.
Where a single spring is fitted, this is sometimes of small
diameter, but it depends upon its position and the space that can
be economically provided. Similarly, the number of coils varies
greatly ; partly, of course, because of the variation in the spring
diameter. But knowing the load (W) and the approximate mean
diameter of helix (D), the size of wire required can be ascertained
from one of the following equations, depending upon whether
round or square wire is to be employed.

0-39 /.

: for circular section.

CLUTCHES AND BBAKES 257

= ^ WD

8 = \ -___-- for square section.

The value of fg for a carbon steel should not be more than
60,000 lbs. per square inch (42*2 kilos per mm.^).

The number of free coils used must depend upon the space
available, but every endeavour should be made to provide as large
a number as possible since the clutch can be more easily operated.

This is due to the fact that when declutching the spring is
compressed, and an increasing force must be impressed on the
pedal by the driver in order to effect this, so that driving through
traffic might become excessively arduous. Hence, the spring must
be checked to ascertain the extra load required for declutching.
The total deflection for the given load W may be found from —

A = -c^-Ti— for circular wire.

= — r-r-i — for square wire.

N may betaken to be 13 X 10^ for a good carbon steel spring,
and n is the member of free coils. This gives the total deflection
for the initial load required to take up the drive, the movement of
the clutch number to effect disengagement will be an additional
amount x (say),

Then A + x = ^ ^t^^ for circular wire

= — :^—^ — for square wire

from which the value of Wi, the actual force on tne spring when
declutched, can be readily ascertained and should be such that
the force on the clutch pedal does not exceed 40 lbs., preferably
less. If more, either the number of coils or the diameter or
helix should be increased. The spaces between the helices should
be such that they will allow about 25 per cent, extra load without
touching. Reference to p. 147, where a worked example is
shown should make the method quite clear.

The ends of springs should be supported on a hardened steel
washer or a ball-bearing if the part which takes the thrust has
any motion relative to the spring when declutched (see Fig. 37 ,
front end), but. if not, it is sufficient that the spring is maintained

M.C.E. 8

258 MOTOR CAR ENGINEERING

symmetrically about the axis of the shaft by means of a collar
(Fig. 88, rear end). Means for the ready adjustment of the
spring load are desirable.

148. For plate, disc, and expanding clutches, an oil-tight
casing must be provided for the retention of the lubricant, and
this requires at least one oil hole of fairly large size, say, about
IJ in. (30 mm.) diameter. Oil is generally employed for
lubricating purposes, and one can generally rely upon the efficient
lubrication of all the enclosed parts from this, but occasionally
graphite is recommended, although it is difficult to realise that it
can give such excellent results as oil, since it usually tends to
form hard ridges and thus conduces to irregular wear.

It is imperative that a universal joint is fitted between the
clutch and the gearbox, or at least a sliding coupling, so as to
permit of the self-adjustment of the clutch and the gear shafts.
In some cases, this is given small dimensions, but it is preferable
to make the flexible coupling as large as those after the gearbox,
although the work which it has to do is not so great. The ty[)e
of coupling that consists of a split muflf bolted over the ends of
the two shafts which are squared up, is not a good form ; espe-
cially where the pin is fitted through a hole in one of the shafts,
for wear and shock soon make themselves evident by a tendency
to rattle when opening up after changing gear. If the end of
one shaft is barrelled, so as to allow a certain freedom of move-
ment, its defects are not so pronounced and it probably suffices
for engines mounted on a subframe. There are manj'' types of
coupling (in some designs two couplings are provided, and this
is to be commended), see Vol. I., and Figs. 88, 40, etc., to
which the reader should refer as well as to Art. 177, for their
design.

149. To determine the maximum load upon the clutch levers,
etc., it is necessary to work from the pedal ; since, although the
normal force applied should not exceed, say, 40 lbs. (18 kilos),
yet, under some circumstances, considerably greater forces may
be instantaneously exerted. The load applied at the pedal should
therefore be considered to be not less than 150 lbs. (68 kilos)
= F = the weight of an average man. The stress induced in
the pedal lever will be greatest near its junction with the boss,
and the bending moment may, for all practical purposes, be
taken as F multiplied by the distance between the point of appli-

CLUTCHES AND BRAKES 259

cation of the force (the centre of the pedal) and the centre of the
shaft, and since the lever is usually rectangular —

F D = i/ew^y

where h is the breadth and h the depth of the section. In
some cases h may be made the same dimension as the boss and
the value of h found by substitution, but b should not be less
than \h, and better, about ^h, so as to ensure stability. The
stress should be taken to be about 7,000 lbs. per square inch.
(4*92 kilos per mm.), otherwise the gear looks rather flimsy, and
unless the proportions above recommended are used the lever
is apt to bend sideways. The lever will taper off to such dimen-
sion as is suitable for the attachment of the pedal. If the levers
actuating the .clutch are made of equivalent cross-sectional
dimensions to the pedal lever, they will be sufficiently strong —
the depth may remain the same and be reduced to j or § that
of pedal lever, since these are much shorter and therefore more
stable. The ratio of the lengths of these levers will depend on
the strength of the spring used, as if directly coupled to the
clutch spring the ratio of force on the pedal must be capable of
overcoming the resistance of the spring to compression. The
shaft upon which these levers are placed is subject to combined
bending and twisting, but it is designed from a consideration of
rigidity, and the ideas of the designer usually determine the
dimensions given. It is most frequently of tubular section on
account of the resistance thereby offered to both forms of stress.
Bosses on levers should be about twice as long as the diameter
of the shaft and should be secured by keys to the shaft.

The attachment of the levers to the clutch should be always
through the medium of a ball-bearing, and various designs are
illustrated both in this volume as well as Vol. I. Clutch brakes
should also be fitted excepting, perhaps, where a disc clutch of
small diameter is used, and is of two principal forms- -that in
which a cone fixed on the clutch shaft engages with another
and fixed cone; and that in which a disc carried by the shaft is
pressed against a pad carried on a flexible bracket secured to the
gearbox and cross girder — the latter gives a more graduated
control over the speed of the clutch shaft than the former, which
is, however, of more compact design. Reference to the various
illustrations in this work will show the details of several forms.

150. Brakes. — Brakes may be divided into two classes— the

s 2

260

MOTOR CAR ENGINEERING

external and the internal — the former being used exclusively for
the propeller shaft brake and the latter largely for rear wheel
brakes.

From the manner in which the car is arrested, by the brakes,
it is obvious that heat-resisting substances must be employed,
and, hence, metal to metal surfaces are largely used, but raybestos
is occasionally fitted to the shoes. With the latter it is impor-

FiG. 42.— Wolsiley Propeller Shaft Brake.

tant that the rivets securing the material are well below the
surface of the asbestos, otherwise an exceedingly high pressure is
generated, which gives rise to noise and causes scoring. The
brake shoes are generally of either steel stampings, cast-iron, or
malleable cast-iron, but if of steel or malleable iron, cast-iron
liners should be riveted to them. The liners should always be of a
softer metal than the drum in order that wear may be largely con-
fined to them — coppdr, gunmetal or bronze liners being frequently
fitted to the brake shoes, giving excellent results, especially the
bronze. Raybestos also is used with satisfactory results. The

CLUTCHES ANP BRAKES

'161

shoes for external brakes should have ribs cast on the back which
assists in keeping down the temperature, by providing additional
radiating surface ; incidentally, these ribs strengthen the shoes.
The drums are now largely made of pressed steel, but cast-iron
and malleable cast-iron are both used for this purpose.

151. Operating Gear. — The actuating gear may operate through
stranded steel cables or through rods— the latter are, however, pre-
ferred, because of the greater security of attachment, their positive
actionand their freedom from any need for attention. Cables, how-
ever, have the advantages that they may be taken over fairleads

262 MOTOR CAR ENGINEERING

where a straight lead is inadmissible and bellcranks may
thus be entirely avoided : on the other hand, the fairleads are
seldom made suflSciently large in diameter' to prevent excessive
bending of the cable and thus the weakening of the material
of which it is composed. Stranded wire is largely employed
for the rear brakes. The shoes are operated either by means
of levers as in Fig. 42 or by a cam which may be as in
Fig. 44. For the rear wheel brakes, seeing that two brakes are
operated by one lever and so far as possible an equal braking
effect is desired on each wheel, some compensating gear is neces-
sary, as is also the case for front-wheel brakes. This is generally
arranged for, with rear brakes, by connecting the rod or wire
from the hand lever to the centre of a lever the ends of which
are directly secured to two other levers, each being attached to
shafts, to which the levers operating the cams are connected.
Modifications of this are often used, but the principle remains the
same in all. At one time, it was the general practice to mount
the change speed lever and the brake lever on the same axis,
hollow shafts being provided as necessary to enable this to be
done, but it is preferable to arrange for separate shafts for
each, otherwise the gear lever has a tendency to become jambed
when the brake is on.

The usual arrangement is for the propeller shaft brake to be
operated by the pedal (see Fig. 45), and for the rear brakes to be
operated by the hand lever, but in some designs both brakes
are on the rear wheels, one brake being placed inside the
other. The object of the latter is to avoid braking through the
transmission gear, and it will be seen that both pedal and hand
operated brakes will require a balance gear. All brakes, no
matter where applied, should have some ready and accurate
means of adjustment provided, and such should always be in
an easily accessible position. Various methods will doubtless be
readily seen, and Figs. 42, etc., show means adopted in four
cases. Figs. 43 and 44 show representative methods of mount-
ing the brakes and the operating gear, so nothing further need
be said under this heading.

152. Design of Brakes. — The braking surface required for any
car is quite independent of the horse-power of the engine but should
vary with the weight of the vehicle on the braking wheels. Too
much surface cannot, however, be given, provided that by so

CLUTCHES AND BRAKES 2fi3

doing tliey are not made either cumbrons or heavy ; since, brakes
are, or rather should be, gradually applied, and hence with a
large area the intenBity of presaure is lees and consequently
the wear on the mechaQiem, thereby prolonging the life of the
gear. Further, the larger surfaces make for smoother braking
action, because the brakes keep cooler. Any brake, practically,
will bring the car to rest if sufficient time is allowed in which
it may do so, but as it is desired that this should he as short
as possible, gear with the maximum braking effect should be

FiLi. 44. — Arrostrong-Whitworth Renr ISrakew.

fitted. The limit to the braking is reached just before the
tyres commence to sUp upon the ground, the friction of rest
being greater than that of motion, and the maximum value of
the co-efficient of friction between the tyre and the road is about
0"65 (the actual value, will, of course, depend on the kind of
tyre and the nature of the surface of the road), but in general it
will lie between 0'4 and 0*5, and a mean value 0'45 will be assumed
for design purposes. Hence, if W is the weigh ton the rear wheels
(or the braking wheels), and R is the radius of the road wheel
— the braking force is Wi^ and the braking torque = Wi/iR. The
value of Wi will depend upon the tyre and weight of body and its
capacity, but its probable value can be fairly closely estimated, as

264 MOTOE CAE ENGINEEEING

can also E since this should be dependent upon horse-power and
the load supported.

Knowing, therefore, the limit to which braking can be carried,
it is only necessary to find what area under a given intensity of
pressure is required to reach this value, the maximum force
required to operate by the pedal being 40 lbs. (18 kilos), and by
the hand lever, say, 20 lbs. (9 kilos). The coefficient of friction
between the shoes and drum will range from 0*15 and 0*2,
probably it is safe to take it as 0*15 for rear whe^l brakes (upon
which oil or grease is frequently deposited) and as 0*2 for the
propeller shaft brake.

158. Propeller Shaft Brakes. — Considering the propeller shaft
brake, and assuming the arrangement is as seen in Figs. 42 and
48, the pressure (P) on the pedal will be increased by trans-
mission through the actuating levers to a force 7iPon the adjust-
ing screw A (Fig. 42). The actual distribution of pressure at
the brake is, however, obscure. If contact were made by the use
of two rubbers of very small circumferential length under the
middle of the brake shoes, the total pressure would be about
twice that on the adjusting screw. If the length of the rubber or
liner is increased by the same amount on each side of the centre
the total pressure would remain the same so long as the shoes fit
closely round the drum, but its distribution would be modified ;
it may therefore be assumed that the total pressure is to the load
on the screw inversely as the distance from the fulcrum to the
projection of the centre of the bearing area of liner on a
diameter through the fulcrum is to the distance from the
fulcrum to the projection of the adjusting screw on the same dia-
meter. In most, if not all designs, this total pressure may be
taken to be twice that of the load on the screw, and hence the
pressure is 2nP. The braking force is therefore 2nP/u:r2 where
^ is the coefficient of friction between the liner and the drum
since the pressure 27iP acts on both shoes, and the braking
torque is 47«PyLtr where r is the radius of the brake drum. By
transmission through the differential the torque on the driving
shaft will be multiplied by x — the gear ratio employed — and will
therefore equal 47iPyLt?*x.

Hence,

4wPyLtrx = Wi/iE

in which n and r are unknown.

CLUTCHES AND BRAKES 265

If the value for r is assumed n may be calculated, but r should
be determined in conjunction with n. The total pressure on each

brake surface is 2nV so that — ;r- is the unit pressure (i>) on the

brake drum, where h is Ihe breadth of the bearing surface. From
an examination of contemporary work, the value otp varies from
70 to 100 lbs. per square inch (0*0492 to 0-07 kilo per mm.^),
so that

2rtP = pi'h

since 2nP is applied to each shoe.

Substituting above —

2pb}^fjLX = Wi/LtR

in which b and r are the only unknowns and the value of ft^-^may
be calculated, the magnitude of each being separately adjusted.

An example will be shown to illustrate the method.

Let the weight on the rear wheels be 700 kilos and the gear
ratio in differential be 3*8 to 1. Diameter of tyres = 810 mm.
To find the size of propeller shaft brake.

2 X 0-06 X hi^ X 0-2 X 3-8 = 700 X 0*45 X 405

hi^ = 1,400,000
Let b =L 55 mm.

Then b)^ = 1,400,000
r" = 25,450
r = 160 mm. = 320 mm. diameter (12'6 in.).

If the higher limit of pressure had been used the diameter would
be 295 mm. (11*6 in.), and if the lower limit, 352 mm. (13*85 in.).

Further, since 2nP = jyrb

2/1 X 18 = 006 X 160 X 55
n = 14-7.

Hence, the ratio of the levers between the adjusting screw and
the foot must be proportioned so that they will multiply the force
in the pedal by, say, 15 to 1. Since the movement of the end of
the actuating lever will be correspondingly reduced from that
at the pedal, and (in the design shown in Fig. 43) this move-
ment will be divided between the ends of the two brake shoes, it
should be observed whether or not a sufficient clearance is
given to the shoes in the off position. The maximum reduction
in travel of any brake gear will be found to be about 25 to 1

266 MOTOR CAR ENGINEERING

if ample clearance is given at the shoes without excessive
movement of the foot,

154. Road Wheel Brakes. — The brake surface for any other
type of propeller shaft brake may be obtained in a similar
manner, and, by the omission of the gear reduction factor x
and the substitution of 2, as there are two acting brakes, that for
the road wheel brakes also.

Therefore ipbi^fi = Wi/LtiR/i. in this case is 0*15, but the
other symbols have their previous significance and magnitude,
except that for p an increase of 60 per cent, is permissible if
there is a propeller shaft brake operated by pedal, because these
brakes are supplementary to the propeller shaft brakes and they
are not used over long periods with the car in motion.

The total force acting each brake surface is as before 2> r b

which, as there are two brakes, necessitates a pull on the end of

lyvh
the shoe of ^-^r-. Therefore, if wi is the multiplying effect of

levers and the cam operating the shoes, the pull on each end

jyj'b 'Vrb

of lever is ^ and the total force on c is ^- ' Hence, if n

2ni 7*1

is the multiplying effect of all the levers, the force (P) applied

to the hand lever is ■ — and prb = 7iP, from which n can be

determined.

155. Brake Cams. — In determining the multiplying effect of
levers for the brake gear no difficulty should arise, but where cams
are employed as seen in Figs. 43 and 44 it may not be quite
clear.

Dealing first with the type of cam ^en in Fig. 44. These are
of the fiat type and are rotated by the levers placed as seen, thus
pressing out the brake shoes. In the position of rest, the two
fiats on the cam rest against the ends of the shoes. The twisting
moment on the cam is the force in rod multiplied by the
length of the lever, and is equivalent to a force T acting at
radius m where m is the distance from the point of contact to the
centre of the cam, that is, one half of the diagonal dimension of
the cam. The effective part of this force T is, however, only in a
direction at right angles to the diameter through the brake shoe
pivot, and the magnitude of this is T cos a where a is the angle

CLUTCHES AND BRAKES 267

through which the cam has turned. The value of cos a from to
30 degrees is from 1*0 to 0'866, and, therefore, the effective pressure
will vary from T to 0"866 T between the angles considered, but as
25 degrees represents the angle through which the cam will turn
under normal conditions and cos 25^ = 0"9063, it is probably safe
to take the effective force as 0*9 T. Hence, the multiplying effect
of the lever and cam is 0*9 of the ratio of the length of lever
to the semi- diagonal of the cam.

For cams which are of the face type in which rollers
pivoted upon lugs on the brake shoes engage with the face
of the cam, so that on rotating the camshaft these rollers are
pushed towards the centre of the shaft and cause the shoes to
engage with the drum, let the angle of thecam(that is, the angle
between the face if unrolled and a line at) right angles to the axis
of the shaft) at a radius n be ^, then the distance moved by a
point on the cam at radius n is — circumferentially 27r/i and
axially 277?i tan ^. The end of the lever on the camshaft
will move through a distance 2tt1. Hence, the mechanical
advantage of the lever and the cam is

2771 1

27rn tan ^ n tan ^

156. Brake Springs, Levers, Rods, etc. — The springs used to
release the brake shoes have very little work to do other than to
overcome the friction in the mechanism, but in a foot-operated
brake they must also raise the pedal ; in which case it is preferable
to fit a supplementary spring for this purpose not far removed
from the pedal, since in that position the strength of the springs
can be much reduced. The size of wire, diameter of heUx, etc., of
the spring may be determined by calculation after assuming that
a certain force is necessary to overcojne the friction, but it is
probably quite as satisfactory lo fix them by judgment, as this
force will vary considerably.

As for the clutch levers and rods, the strength of the brake gear
must be determined by working from the pedal or from the hand
lever. It may be assumed that a force of 150 lbs. (68 kilos) is
applied to the pedal and one of 50 lbs. (23 kilos) to the hand lever.
Then the load on the rods (which should always be in tension) or
wires will vary inversely as length of the lever to which it is

268 MOTOR CAR ENGINEERING

attached and from which it deriven ils motion. Tliim. the lond o
rod will be

I . /LeURth of lever A\

\Leitgth of lever li/ '

The levers will be designed for bending in the plane of motion,
t)ie load being that on the rod secured to it and the section

Fi<3. 4,).— Wolseley Faial Gear,

considered being close to the boss. The bending moment nill be

Load (l — I, where 1 is the length oE the lever and 8 is the

diameter of the boss. Equating this to the moment of resistance
—the stress being about 8,000 lbs. per square inch (5-62 kilos
mm. 2 ) — the dimension of the levers may be determined. The
breadth of the levers should be from 3 to 4 times the width.

Shafts subject to torsion will he designed for a twisting
moment of (Load on end of lever attached to shaft x length of
lever) imd the moment of resibtiiiice will be

according ns solid or hollow shafts are employed. The shaft

CLUTCHES AND BRAKES 269

should be made so that the minimum radius (to the bottom
of the keyway) is not less than one-half of the dimension
obtained. Key should be proportioned in the usual manner on
the diameter of the shaft, but should be checked for shear as
shown in Art. 192.

breadth = 1^ + ^j-t; to J

depth = Jd + jg to J

All pins are subject to double shear, but their strength is only
If times that of single shear, because of the bending of the pin.

The stress is -^-j — and should not exceed, say, 7,000 lbs. per

square inch (4*9 kilos per mm.^). It, is, however, very desirable
to provide ample bearing area, as the large number of pins at
which wear will take place makes it essential that every effort
must be made to reduce its magnitude so far as possible, other-
wise frequent adjustment will be necessary. In many designs,
these parts are provided with bronze bushes which may be easily
replaced when wear takes place.

Means for adjustment of the brake shoes and the position of
the pedal are essential and should be fitted in a readily accessible
position.

The lubricating devices need be only of the simplest nature
as movement is not great, but it is best to fit a dust-tight cap
or clip to prevent the entry of grit into the pins or bearings.
For the parts which are not in a position to which ready
access can be obtained, it is advisable to use grease cups — more
especially for long shafts or tubes for the road-wheel brake
compensating gear.

CHAPTER XIV

GEARING

157. Probably in no other part of the chassis has there been
such great improvement without apparent change than in the
gearing employed, which now has reached a high standard of
excellence. The difficulties encountered have been twofold.
Firstly, the production of the correct shape of tooth was not pro-
duced by the machines at one time available. Tliis has been
overcome by the invention of several tooth-generating machines,
and by the extended use of cutters by means of which the wheel
teeth are automatically cut to the correct shape. Secondly, when
a tooih of correct form was obtained, on account of the severe
conditions of use, high speeds and heavy loads, wear soon
destroyed the perfect action between the teeth, while if harden-
ing was resorted to, the accompanying distortion was such that
it nullified the advantages accruing from the use of modern gear-
cutting machinery, and necessitated the grinding and trimming
of the teeth. With the steels now available, however, greater
advantage can be taken of these self -generating machines as the
distortion in hardening is small, while in many grades the metal
is sufficiently hard to require no further treatment, and thus,
together with such materials as bronze, are able to reap the full
benefit. It is therefore necessary to indulge in a large amount
of hard work in fitting gears, if a good machine is used in cutting
the teeth ; in fact, noise and vibration are often directly traceable to
this, for the teeth, as finished by the tool or cutter are as nearly
the correct form as it is possible to make them, and any filing or
scraping is as likely to remove the metal from the wrong part as.
not, while grinding acts equally on all surfaces. Hence, given
the correct tooth form and providing that the design is good, it
will naturally follow that the gears will work quietly, smoothly,
efficiently, and give -little troubleeven over longperiods. These then
are the conditions to be fulfilled for successful operation, and both
must be considered here, as there are so many factors influencing

GEARING 271

the shape of tooth quite apart from the actual process of cutting
the tooth that enter into the question of design.

It is not proposed to enter into the question of cutting the teeth,
but the reader may refer to Mr. Stevens' paper on " Tooth
Gearing " for information on the subject.

158. Types of Gears. — The choice of gears is somewhat restricted
by the direction in which the shafts that are to be coupled
together lie. If the axes of the shafts are parallel, spur, helical or
chain gearing may be adopted, and if at right angles, then either
bevel or worm gear may be employed, while for inclined shafts
either bevels, if the axes intersect, or skew.gears if they do not, are
used.

The question is not altogether one of efficiency, for all these
gears may be made to be very satisfactory in this respect, but
it is in regard to cost, degree of silence, durability and general
convenience that one form has an advantage over another. Worm
and skew gears are very quiet, and retain their good qualities for a
long time, but are expensive to manufacture and need careful
attention to the methods of mounting and lubrication for a high
efficiency. Bevel gears are more easily cut and fitted, but are
noisier and lose their efficiency at a more rapid rate. Helical
gears, a form of spiral gears, are more expensive to cut than
spur gears, especially when of the double form, and are not
adapted for use in all situations, as, for example, in change speed
mechanisms, but they are smoother in action, and stronger and
more durable than spur gears. Chain drives are mainly employed
where the load does not vary greatly, and give extremely quiet
smooth operation with a high efficiency ; but necessitate the
employment of some adjusting gear where the relative positions
of the driving and the driven shafts must be maintained, are not
easily adapted for employment in gearboxes, because the centres
of shafts are at constant distance, and one chain may be initially
of different length to another or may, in course of time, become
so through ununiform stretching or wear. These are the main
points in connection with gearing, but others will be referred to
later as the particular types are considered.

159. Shape of Teeth. — There are an indefinite number of
shapes of teeth that could be used for gearwheels, and give
correct tooth action, but only two forms are used in practice for
spur, bevel, worm and helical gearing, and these are termed the

272 MOTOR CAR EiNGINEERING

" involute" and the " cycloidal," but by far the greater number of
gears have an involute tooth.

If a flexible cord is unwrapped from round a cylinder, the end
of the cord if kept tight would trace out an involute to the circle.
If a circular disc is caused to roll upon the circumference of
another circle, the locus of a point on the circumference of the
rolling circle is termed a cycloid. When the rolling circle is with-
out the other the curve is an epicycloid, and when within the
the circle, a hypocloid. The methods employed in drawing
these curves may be seen in any elementary textbook on Plane
Geometry, or in Unwin's " Elements of Machine Design," Part L,
but Ihere are several points to which reference may here be made.
Tlie first is, it should be noted that every diameter circle will
have a different shape of curve for its involute, and that the
shape oi both the epicloid and the hypocloid will be dependent
upon the diameter of the generating circle and the base circle.
The second is, that the normal to the curves at the point of
contact passes through what is termed the " pitch point." This
is the condition which must be satisfied by any toothed wheels
for constant velocity ratio. Tiie third is in regard to the line
of contact of the meshing teeth. Before these several points
are explained it is desirable to define the various terms employed
in connection with them.

The pitch circle is an imaginary circle of such a diameter
that when any pair of wheels are correctly meshed together it
passes through a point on the line adjoining the axes of the
wheels, such that the distance apart of the two axes is divided
in the ratio of the number of teeth in each wheel.

The pitch point is the point of intersection of the pitch circle
with the line joining the axes of the wheels.

The addendum or jwint is the height of tooth above the pitch
circle. The addendum circle passes through the tops of the
teeth.

The dedendnm or root is the depth of tooth below the pitch
circle.' The root circle passes through the roots of the teeth.
The angle of obliquity is the angle between the normal to the
surfaces in contact and a line at right angles to the line of centres.
In the case of cycloidal teeth this varies during contact from
degrees up to a maximum depending upon the diameter of the
rolling and base circles, but in involute teeth it CTO be paade

GEARING

273

whatever value is desired, and is then constant throughout the full
range of contact.

160. Cycloidal Teeth.— Considering Fig. '46, the circles XPY,
MPN represent the pitch circles of two wheels, and APB, CPD
the rolling circles. The dotted lines represent the addendum and
root circles of the two wheels, while P is the pitch point. Now
if these circles are per-
mitted to roll together
on their axes, the curve
traced out on each wheel
will be a cycloidal curve,
the point V on the upper
rolling circle will move
to P, and P on the lower
will move to T, along
the arcs VP, PT respec-
tively, and hence VPT
is the path of contact.
VP is termed the arc of
approach, and PT the
arc of recess. The
cycloidal curve traced
out by the circle APB
on the upper wheel will
be the curve VW — a
hypocycloid, and on the
lower wheel VU — a n
epicycloid, and these ^^o- 46.— Cycloidal Teeth.

curves have been generated by the » one circle in moving
from V to P, and in a similar manner the curves TR and TS
will be generated by the lower circle in moving P to T.
Hence, since P is the instantaneous centre of rotation of the
rolling circles relative to the base circles, the normal to the
two surfaces in any position passes through the pitch point,
and these curves will roll uniformly together during approach if
the dedendum of the upper wheel and the addendum of the
lower wheel have the same rolling circle, and during recess if
the addendum of the upper wheel and the dedendum of the
lower wheel have the same rolling circle. It will be noted that
it is not necessary though it is usual for both the flank and

M.C.B. T

274

MOTOR CAR ENGINEERING

root of any one tooth to be generated by the same diameter
rolling circle, and further, that in moving from V to P, the point
of contract moved from V to W on the upper and from V to U
on the lower tooth, the difference in these two lengths represents
the amount of sliding during approach. Also, it will be seen
that the angle of obliquity changes from a maximum at Y to zero
at P, and then increases to a maximum at T, the angle of
obliquity at approach being less than that at recess with unequal
diameter wheels and the smaller driving. The maximum angle of
obliquity is usually 30 degrees, otherwise the thrust on the bearings
is excessive as a straight line from Y to P — that is, the normal at
the point of contact is the line of action of the force causing
rotation.

It will be noted that the smaller the rolling circle, the nearer
will Y approach the line of centres, and hence the greater the
obliquity, while the larger the rolling circle the less the obliquity,
but when the rolling circle is one half the diameter of the pitch
circle the cycloid becomes a radial line and produces a weak
root section. Therefore it is usual to make its diameter not less
than one fourth nor more than one half the diameter of the smallest
wheel in the train.

TABLE XY.
Cycloidal Cutters.

Letter.

A
B
C
D
E
F
G
H

Number <>f Teeth
iu Wheel.

Letter.

Number of Teeth
in Wheel.

Letter.

21 to 22

23 to 24

26 to 26

27 to 29

30 to 83

34 to 37

38 to 42

Number of Teeth
Wheel.

43 to 49

50 to 59

60 to 74

75 to 99

100 to 149

150 to 249

250 or more

Rack

Next, it is clear that the same rolling circle should be used for
all teeth in wheels in the same train, otherwise inaccurate action
must result, while the variation in the shape of the cycloid with
variation in the diameter of rollincr circle necessitates the use of

GEARING

276

cutters of different form with wheels having the same pitch of
teeth but of (Hfferent pitch circle diameter, that is, with a
different number of teeth. To fully meet this difficulty an infinite
number of cutters would be necessary, but in practice twenty-
four are standardised by Brown and Sharpe, and are found to
meet practical requirements.

There are thus 24 cutters to each pitch of tooth, and when the
pitch has been settled a suit-
able shape of cutter must be
selected from the above table
with which to cut the tooth.

161. Involute Teeth. — In
Pig. 47 XPY, MPN are the
pitch circles of two wheels
and AGB, CHD are base
circles, the other dotted lines
being the addendum and de-
dendum circles respectively.
In involute teeth the angle of
obliquity is constant and is
therefore represented by a
straight line BPS through
the pitch point and making
an angle BPF equal to the
angle of obliquity with the line
at right angles to the line of
centres. The circles AGB,
CHD have been drawn so
that BPS is an internal tan-
gent to them at the points
B and S, so that if the
two pitch circles roll together the curves traced out by the
points B and S on the wheels will be involutes to the two base
circles. B will trace out BK on the upper and BL on the
lower wheel in moving from B to P, while S will trace out SO
on the upper and SQ on the lower wheel in moving from P to S.
Hence, teeth generated in this manner will roll together and give
constant angular velocity, since the normal BS will always pass
through the pitch point SP because the line drawn tangent
to the base circle from any point on the involute is a normal to

T 2

Fig. 47.— Involute Teeth.

276

MOTOR CAR ENGINEERING

the curve. As before, the difference in the lengths of RK and
RL is the amount of slidijg between the teeth in moving from
R to P. The length of contact is RL or SO, and RPS is the
path of contact.

It will be seen that if the wheels are displaced so that the
pitch circles do not intersect at the same point P the involutes to
the base circles will remain of the same form, and the normal at
the point of contact will always intersect the line of centres in a
point that the distance between the axes of the wheels is divided
in the ratio of the number of teeth in each wheel. Hence, if the
centres are displaced, through wear at the bearings, it will not
affect the correct action of the teeth.

The angle of obliquity may be made from 14^ degrees and
20 degrees, but Brown and Sharpens standard is 14^ degrees ; but
there is another standard in which the angle is 20 degrees. (See
Art. 164.) A great advantage of the involute tooth is that
all wheels of the same pitch and the same angle of obliquity will
gear correctly with one another and that the thrust is not so
great if the 14| degree standard tooth is employed. It is usual
to make the flank of the tooth from the base circle a ] adial line.

Since the shape of the involute varies with different diameters
of base circle, a series of cutters have been standardised by
Brown and Sharpe for each pitch as follows : —

TABLE XVI.

Involute

CUTTEKS.

Number of

Number ofTeelh in

Number of

Nui

iiber of Teeth in

■ Cutter.

Wheel.

Cutter.

Wheel.

135 to Rack

21 to 25

80 to 134

19 to 20

55 to 134

17 to 20

42 to 54

15 to 16

35 to 54

14 to 16

30 to 34

26 to 34

12 to 13

28 to 25

ut the half sizes can

The whoh

9 numbers are the u

sual sizes, b

be obtained

when extreme acci

iracy is req

uired

in the work.

GEARING 277

There are thus fifteen different cutters for each pitch, and when
the pitch and number of teeth are determined the suitable cutter
should be selected from the above list.

The particular case of an ordinary worm should be observed.
Here the base circle is a straight line parallel to the axis of the
worm and is therefore a circle of infinite radius. The normal to
the thread at its point of contact with the teeth of the wheel is
therefore inclined at an angle with the axis of the shaft and the
flanks are straight lines, the two sides enclosing an angle of 2d
where is the angle of obliquity.

General Note. — The need for extreme accuracy in setting out
gear teeth cannot be overestimated, and where cutters of any
kind or hobs are employed unless of standard form, the greatest
care must be exercised in determining the shape given to them,
otherwise the satisfactory operation of the gears is jeopardised.
Principally for this reason a large number of manufacturers
entrust the cutting of their gears with firms who specialise in
this work. In dimensioning drawings of toothed wheels the
diameters, etc., should be given to the fourth decimal place
in English units and to the second decimal place in millimetres.

162. Methods of measuring Fitch. — There are three ways by
which the pitch of teeth is measured — the circular, the diametral,
and the metric.

The circxdar jntch is the distance along the pitch circle between

one point on a tooth and the corresponding point on the adjacent

tooth, or is the distance measured along the pitch circle between

the centre of one tooth and the centre of the adjacent tooth.

Hence, the circumference of the pitch circle = N7), the pitch circle

Ni> ttD

diameter is — ^ and p = -^r^ , where N is the number of teeth, « is

the circular pitch and D the pitch, circle diameter.

The diametral pitch is the number which represents the ratio

between the number of teeth and the diameter of the pitch circle

N
in inches and is t^ ^^ "^^y ^® stated to be the number of teeth

per inch of diameter. If P is the diametral pitch P = - . If

N + 2
the outside diameter of blank is Di, P = ' , and

■1^1

278 MOTOR CAR ENGINEERING

N -4- 2
Di = - p . The distance between the centres of the wheels is

one half the total number of teeth divided by P.

This system is very convenient, and is extensively employed,
because awkward fractions of an inch can be avoided for the
pitch circle diameter. Thus a wheel of 40 teeth of 8P is 5 in.
diameter.

The metric jnteh or module is also largely used in automobile
work, has the same advantages as, and is numerically the
converse of, the diametral pitch. If M is the module, then

Thus, a wheel of 40 teeth of 8M is 120 millimetres in pitch
circle diameter.

163. Minimum Number of Teeth.— With cycloidal teeth if the
maximum angle of obliquity is 80 degrees. Professor Dunkerley *
has shown that the number of teeth should not be less than 12
when the rolling circle is one half the diameter of the smallest
wheel in the train, and if one quarter of the smallest wheel, the
minimum number is 24.

With involute teeth having an angle of obliquity of 14 J degrees
the minimum number of teeth is 24, and with 20 degrees angle of
obliquity is 17.

These numbers are true for two pairs of teeth to be always in
contact, and if a lesser number of teeth is employed the arcs of
approach and recess will be shortened, and hence only one pair
will be always in contact. This is to be guarded against because
not only does one tooth of necessity take the full load, but wear
is more rapid, and therefore the durability of the gear is likely to
suflfer unless much larger proportions are employed than are
usual. In addition there is a large amount of undercut which is
necessary in order to clear the tops of the teeth and therefore
precludes the use of a milling cutter for cutting the teeth. As a
general rule it is desirable that in no case should there be less
than 20 teeth, and preferably 25, although instances are known
where bevel wheels have but 12 teeth. To increase the minimum
number of teeth in gear the length of the arc of contact must be
lengthened, or the pitch of the teeth reduced without altering the

1 Sec Duukerley's" Muchaiiism."

GEARING 279

addendum height. The former entails the increase of the height
above pitch line, hence the angle of obliquity is greater and the
tooth must be made larger in order to withstand the greater
stress, because the decrease in actual total load on the tooth does
not vary exactly inversely as the height. The latter is objection-
able, because a tooth of § the pitch has only ^ of the strength,
while the actual load is reduced to rather less than two thirds of
the original load. Hence, the proportions given in Art. 164 are
based on experience and have been found to give good all-round
service.

164. Proportions of Teeth. — With machine-cut teeth such as are
used in automobile work there is comparatively little variation
in the proportions owing to standardisation. The following
gives the proportions of a Brown and Sharpe tooth for circular
and diametral pitches — one that is largely used in this country
and in America — as well as a metric tooth.

Width 5f tooth on pitch _ ^ - _ 1'5708 _ i.c^noM

hne ^ P

Heigh t of tooth above pitch r^^too 1 \t

hne ^ P

Depth of tooth below pitch ^ 3 ^ 14^8 ^ ^.^^^^^ ^

hne ' P

Clearance at foot = 0*05 p = p = 0-15708 M.

Total height of tooth = 0-6866 p = ?i|^ = 2*15708 M.

These proportions are employed for both cycloidal and the
14| degrees involute tooth. The diameter of the base circle with
a 14^ degrees involute is 0*968 of the pitch circle diameter.

The undercutting above referred to with small numbers of
teeth, as well as the desire for a stronger tooth, has led several
investigators to suggest the use of a shorter tooth with a greater
angle of obliquity, and these are now often employed. In these
the height above the pitch line is often made 0*25p and the
depth below OSp, while the 14J^ degrees angle of obliquity may be
retained or increased to 20 degrees, the latter having a base circle
of 0*94 of the pitch circle. Occasionally the height above the pitch
circle is made O-Sj?, and Messrs. Sellers have standardised this
with a 20 degrees tooth, while 22^ degrees has been suggested as

280 MOTOE CAR ENGINEERING

a desirable angle. It is claimed by Mr. Stevens ^ of Messrs. E. G.
Wrigley & Co. that with increased obliquity and reduced height —

(a) It can be used right down to twelve teeth in its true form,

and cut on either a single cutter or generating machine.

(b) It is altogether a stronger form than that most commonly

used at present.

(d) The possible objections on the score of less contact and

greater bearing pressure .are so slight as to be nearly
negligible.

The increased angle of obliquity to 20 degrees will raise the
thrust on the bearings by about 6 per cent., while the manner in
which the arc of contact is reduced will be clear from Fig. 47.
Undercutting is present whenever less than 80 teeth are used
and the teeth are of the 14^ degrees involute form. The effect of
friction at the teeth has been neglected in the proceeding because
it is certain that in automobile practice with lubricated machine-
cut teeth it is insignificant.

165. The Design of Spur and Bevel Gears. — As a general rule the
distance between the shafts of spur wheels is unfixed but can be
closely approximated to after a little practice. The gear ratio
will determine the radii of the two wheels, then knowing the
maximum torque transmitted, the pressure (F) at the pitch line
can be calculated.

It is usual to assume that two teeth carry this pressure, hence
the maximum load on one tooth may vary between JF and F.
The actual distribution is, however, not easy to determine, but
with machine-cut wheels carefully fitted in place, the load on
each tooth should differ very little from JF, especially since the
elasticity of the material must have an equalising effect upon the
distribution. This load can also be regarded as acting along the
full width of the teeth, and the worst condition will be when the
load comes upon the point of the tooth, in which case the greatest
bending stress will be at the root, and if the tooth is created
as a cantilever, the bending moment equals |F1. This is not
strictly true, as the line of action of the force is at an angle of
14J degrees, with the axis of the tooth in 14J degrees involute
tooth, but it is suflSciently so for all practical purposes and the
margin is on the strong side.

1 See "Twjthed (Jearin«,>," Proc. I. Mech. E.

GEARING 281

Then :—

ipi = I bk'f,

where 1 is the total height of the tooth, b is the width, fe is tlie
thickness of the tooth near the root, and / is the stress. A pitch
must now be assumed as near to the pitch that will probably be
used as the designer can make it. Tables and diagrams are often
available to assist in this, and then 1 can be obtained either from
tables or from the formulae given in Art. 164, but h must be
determined separately since it will depend upon the number and
shape of teeth employed. The probable number of teeth will be
known because the pitch circle diameter is known, while the
shape will be decided upon, and hence the thickness at the root
(h) can be estimated. The method here indicated should at
least be followed when the dimensions of the teeth have been
obtained, especially in wheels that have a small number of teeth,
but in general it will be found to be sufficiently accurate at first
for the dimensions at the root to be assumed to be the same as

those at the pitch line, that is 6 will be 0'5p = — p =

1-5708M.

The stress used in the design will depend upon the class of
material, but the factor of safety should not be less than 10 and
preferably 12, or even 15 in the harder grades of steel, since there
is generally a moderate amount of shock. Therefore, b is the
only unknown and may be determined by calculation. Should
this prove excessive — as a wide tooth should be avoided — it should
never exceed 2*5 times the circular pitch, and in gearboxes 1*5
times the pitch is generally the limit, as otherwise the box becomes
too long ; a larger size of tooth must be selected in order to bring
down the width.

But the width must also be considered from the aspect of bear-
ing pressure. Theoretically, the contact is made not on a
surface but on a line, but the yielding of the material will cause
surface contact to take place. In ball- and roller-bearings, the
load carried increases with the diameter, and as the circumstances
are somewhat analogous, it is reasonable to suppose that increase
of pitch (that is, of curvature) will enable higher loads to be
carried per unit of width. For fibre and rawhide wheels of
about 0*75 in. circular pitch (4P or 6M) the pressure should not

282 MOTOR CAR ENGINEERING

exceed 150 lbs. per inch of width (2 kilos per mm.), for bronze
wheels 400 to 500 lbs. per inch of width (5-25 to 7 kilos per mm.)
is permissible, and for hardened steel wheels from 1,500 to
2,500 lbs. per inch of width (20 to 88 kilos per mm.) is often used.
Therefore, since the load on each tooth is JF, the load per

unit of width is ^, , and this should not exceed the figures given

above. With a little adjustment combined with judgment, suit-
abl<3 dimensions for the teeth can be obtained to answer both
requirements — strength and bearing pressure.

166. In bevel wheels the pitch surfaces are conical, and any
pair of bevel wheels which are to be geared together must have
a common vertex — the point of intersection of the axes of the
wheels. The line of intersection of this surface with the outer
end of the teeth, that is, at the largest end, is the pitch circle.
In getting out the dimensions of a pair of bevels, the pitch circle
diameter can be closely approximated to, as can also be the
probable width of tooth. The angles of the pitch cones or
surfaces will be determined by the gear ratio employed, quite
independently of the size of the wheel. These should be drawn
out, and the radius (r) from the centre of the smallest wheel to
the middle of the assumed length of the tooth on the pitch line
determined therefrom — this will be the mean radius of the pitch
line of the bevel. When transmitting torque the wheel teeth
will be deflected by the pressure upon the point of the teeth, and
the magnitude of this deflection will have the same ratio as the
radii from the axis of rotation to the points considered on the

1 WP

tooth point. The deflection of a cantilever is ^ ^r^, and I =

:r-z hlfif therefore, as j varies, eo will the load vary in like manner,

but J is as the radii from the axis of rotation to the points con-
sidered on the top of the teeth, hence the load will vary in the
same proportion. But the equation of strength for a cantilever

1 (Wl

is Wl = T7 W/y, and/ = tt^, so that if Wi, 1 and li vary in a

similar manner the stress will be the same, and hence, since the
load, the total height of tooth, and its thickness at the pitch line

GEARING 283

vary as the . addendum radii, the stress will he the same
throughout.

From the above it is seen that the load varies as the radii and
r is the mean radii, hence the bevel wheel may be designed so as
to obtain a section of tooth at radius ?* that is capable of trans-
mitting the torque required. Knowing therefore the radius r
and the maximum torque, the design resolves itself into a similar
problem to the design of a spur wheel as above, b being the total
length of the tooth, the section found being that at the middle of
the length of the tooth. The same rules will apply as to strength
and bearing pressure as were used for spur teeth. To obtain
the dimensions at the outer end of the teeth it is only necessary
to set out the figure in its correct position and draw lines to
the point of intersection of the driving and the driven shafts —
the dimensions will be proportionate to the distances of the
sections from this point. The manner in which the face angle
is obtained either by calculation or graphically is obvious and
requires no explanation. Bevel wheels cannot be cut correctly
with rotary cutters, but require a generating machine, preferably
of the self -gen era ting type.

In both bevel and spur wheels, the teeth depend for their
perfect action upon the rigidity of the rim upon which they are
placed, hence it is important that this should be of a sufficiently
large thickness. A very good rule is to make the rim thickness
not less than one half the circular pitch of the teeth in spur
gears. In bevel gears the mean tliickness should be not less
than this, the dimensions at the two ends of the teeth being
obtained by drawing a line for the points of intersection at the
axes of the wheels through the point representing the mean
thickness when set off on the drawings

From strength considerations the peripheral velocity of the
teeth need not be considered in automobile practice, since the
stress induced in the rim is always much less than the critical
speed with the materials usually employed, but with linear
speeds of 2,000 ft. per minute it is inadvisable to make the
teeth of less than 8P, otherwise they have a tendency to
" scream."

In some cases, the numbers of teeth in the wheels must bear
a fixed ratio, as, for example, in camshaft or magneto drives, in
order that the revolutions of the camshaft may be rotated at

284 MOTOE CAR ENGINEERING

half the speed, and the magneto shaft at some definite relative
speed to the crankshaft. But in the gearbox and the differential
a definite ratio is unnecessary, and, as will be seen, is undesirable.
Supposing, for example, that the numbers of teeth in the wheels
are 40 and 50. Then every five revolutions of the driving shaft
the same teeth will come into engagement in each wheel, but if
the driven wheel is given, say, 51 teeth, the driving shaft will
have to make 51 revolutions before the same teeth mesh, and
hence, should there be any irregularity in the shape of the tooth,
or if one tooth is harder than another, the wear on the other
wheel will be more uniform, and hence the noise caused by bad
teeth action will be less pronounced. The ratio, it will be seen,
is but little affected, for as first arranged it is 1*25, and after the
extra tooth is added 1'275. Therefore, wherever possible with
any form of gearing, the ratio should be adjusted so that this
action takes place. The extra tooth is termed the " hunting tooth."
167. Helical Gearing. — Helical geaiing is often employed for
camshaft drives, and occasionally for the layshaft drive in the
gearbox, where the whee's are continually in mesh. In both of
these drives they take the place of spur wheels, but it is possible,
though unusual, in cars to employ a bevel form. This gear, it
should be observed, is a form of screw gear, in that the teeth
intersect the pitch surfaces in helices, but the mode of action is
similar to that with spur and bevel gears, as the driving and
driven shafts are parallel. Both single and double helical gears
are employed, but in automobile work the former is generally
adopted, probably because of the difficulty in obtaining contact
on both sides of the teeth.

The total force acting at the pitch lines producing the torque
is in the plane of rotation, bu^. from the angle at which the teeth
are inclined to the axis of the wheel in single helical gears there
is an axial thrust of V tan 0. The normal pressure is F sec 0,
and the actual width of the tooth is h sec 0. Where F is the
tangential force required to produce torque, is the angle between
the tooth and a line parallel to the axis of shaft, that is, the spiral
angle, and h is the breadth of the wheel. The normal pressure
and the actual width of tooth vary with sec 0, and therefore for
bearing pressure considerations the breadth of the wheel may be
determined from F alone.

Now, from the nature of the tooth contact, which extends from

GEARING 285

the point at the leading edge of the tooth to the lowest point of
contact at tlie following edge of the tooth, it is clear that at no time
is the pressure acting on the point of tlie tooth, but it may be con-
sidered to be acting at some mean position. This may be assumed
to be at two-thiids of the height of the tooth, and as there will

1 2

be two teeth in contact the bending moment will be -F X ^ 1 =

— Fl, where 1 is the total height of tooth. By equating this to

the moment of resistance = - W/V the dimensions can be

b -^

determined as for spur gearing.

The angle B should be considered in conjunction with the
breadth of the wheel, since this angle should be as small as
possible in single helical wheels to reduce side thrust, and in
double helical wheels in order to avoid wedge action, but so that
contact is made over the full breadth of tooth. The angle will be
of opposite hand for any pair of single helical wheels. In an
involute tooth, therefore, the angular displacement of the teeth
should be from S to R (Fig. 47), from which the angle can be
determined. The usual rules for the proportions of teeth apply,
the section considered being in the plane of rotation, and this is
the section to which the dimensions obtained above refer.

Provision should be made to take up the thrust along the shaft
by means of a thrust of bronze, as ball thrust bearings are really
unnecessary if the lubrication afforded is sufiBcient, and would
make the gear cumbersome.

168. Worm Gearing. — In worm gearing the shafts are at right
angles, and it is generally employed in ordinary engineering
work where a high reduction is desired, but this is not so in
automobile work, as silence is then the great consideration. The
cutting of correctly formed worm wheel teeth has long been a
problem of great di£Brculty with engineers, but at the present day it
is possible to obtain wheels of excellent form, either by bobbing or
the use of a fiycutter, and much of the disrepute into which the
class of gear fell through wear overheating and low eflBciency can
be rightly attributed to the badly formed and proportioned gears at
one time in use. The expense, too, that was at one time so heavy,
is not now so marked, as manufacturers have specialised in this
class of work, standardising their hobs (Messrs. David Brown

286 MOTOR CAR ENGINEERING

and Sons have over 1,000 standard hobs), and so reduced the
cost that ^ork can now be done at nearly as small a price as
other forms of power transmission.

The shape of tooth employed is generally involute, on account
of the fact that the sides of the worm thread there are straight
inclined to the axis. The 14^ degrees involute is often used,
but a 15 degrees involute is sometimes employed, giving a con-
tained angle between the sides of the thread of 29 degrees and
80 degrees respectively for the two angles of obliquity mentioned.
The proportions of the teeth follow the rules previously given for
Brown and Sharpe standard, excepting when there is an extremely
small number of teeth in the wheel. In this case the same pitch
lines are maintained, but the addendum of the worm thread and
the root of the wheel teeth are reduced, and the addendum of the
wheel teeth and the root of the worm thread increased — thus
preventing undercutting.

The gear reduction is the ratio of the number of teeth in the
wheel to the number of threads on the worm. Thus, if there are
34 teeth in the w^heel and a 7 start worm is used, the gear
ratio is 84 to 7, but if only a single threaded worm is employed
the ratio will be 34 to 1. Spiral gearing is only another form of
worm gearing, the velocity ratio being the number of threads in the
driven worm to the number of threads in the driving worm. In
this form of gears the shafts are not at right angles, but inclined
at some other angle. These threads may be at quite different
an<^les relative to their axis, and may also have different pitches,
but since in drives used in automobile work the shafts are always
at right angles only worm gearing will be considered here. The
design is, however, similar in both forms of gear, the only differ-
ence being in the angle at which the threads are inclined to the
plane of rotation. The true shape of spiral wheels in cross
. section is a hyperboloid, but on account of the narrow width of
the wheels it is usual to make them straight.

Worms may be either right or left hand according to the
direction of rotation required. For worm driven rear axles,
seeing that the direction of rotation of the crankshaft is clock-
wise, the worm should be right handed when placed above
the wheel and left handed when below the wheel. Worms
may also be of the straight form or the hour-glass or the
Lanchester form. The former is more common, and requires

GEARING 2ft7

less fitting, because its position is defined by placing it at the
correct distance from the axis of tbe wheel in a plane through
the centre of the worm wheel and at right angles to the axis,
whereas with the latter it is also necessary, for the plane through
the middle of the length of the worm at right angles to the asia
must contain the axis of the wheel. Hence, greater skill is

i'lo. 48.

required in manufacture and it will only be found in the highest
class of work. But it has the greot advantage that the pressure
on the wheel teeth may be reduced because there are a greater
number of teeth in contact since the worm fits round the
circumference of the wheel for its entire length.

169. Defljiitions. — For a single threaded worm the definitions

288

MOTOR CAR ENGINEERING

given in Art. 188 have their previous significance, but there are
several that should be added, and with multiple threaded worms
the meaning of the term pitch is somewhat altered. Thus, there
are now four kinds of pitch ; circular pitch, linear pitch, normal
pitch, and lead or true pitch.

LEAD INCHES.

■

1 V«

V-

* 1

1 1

\
\

'ft

\
\

^ .

— \

4B=

:» 10 15 20 25 bO Ah 40

DEGREES.

Fig. 49.

Circular pitch is the distance along the circumference of the
pitch circle of the wheel between the centre of one tooth and the
centre of the tooth next to it. Is equal to linear pitch.

Linear pitch is the distance along the pitch line of the worm
between the centre of one thread and the centre of the thread
next to it. Is equal to the circular pitch.

GEARING . 289

Normal pitch is the perpendicular distance between the centre
of one thread or tooth and the centre of the thread or tooth next
to it. Is equal to linear pitch multiplied by the cosine of the
pitch angle.

Ijcad or true pitch is the axial distance traversed by one thread
during one revolution and is the product of the linear pitch and
the number of threads.

Lead or pitch angle is the angle at the pitch circle between the
thread and a line perpendicular to the axis of the worm.

Spiral angle is the angle at the pitch circle between the thread
and a line parallel to the axis of the worm.

The pitch circle diameter of worm wheel is measured in a
plane through the centre of the wheel so that one-half of th^ sum
of the pitch circle diameters of wheel and worm is the distance
between the axes of the shafts.

170. The Design of a Worm Gear. — In designing a worm gear the
velocity of ratio required and the power or torque transmitted at
any speed of revolution is known while the approximate line of
centres can be estimated. Now the theoretical efficiency of a
worm drive is given by the expression : —

P tan a

* """ tan (a + x<l>)

where a and (f> are pitch angle of thread and the angle of friction
respectively and a? is a quantity depending upon the angle of
thread, but x may be neglected since, with a 29 degrees thread, its
value is only 1*08 and <^ is always small compared with a. This

expression is a maximum when a = 46° — ~. Taking the

coefficient of friction as 0*05, the pitch angle for maximum
efficiency is 48^ degrees and the efficiency will increase as the angle
increases until it reaches this value. But the pressure upon the
teeth causes an end thrust upon the worm, and it is found in
practice that the friction on the thrust bearings reduces this
angle considerably, so that about 80 degrees represents the angle
at which the maximum efficiency is reached. Hence, regard must
be had to this value.

Unwinds formula for the efficiency of a worm is : —

j^ 1 — fi cot a

Ifi tan a

M.G.E. U

290 MOTOR CAR ENGINEERING

which gives for this 30 degrees angle an efficiency 88*7 per cent,
which accords fairly well with observed, results.

For worm drives to the rear axles the condition must also be
fulfilled that the gear must be reversible. This is satisfied when
the angle of the thread is not less than the tangent of the
coefficient of friction which if /a = 0*05, as it would be with well-
lubricated axles, is 8 degrees. In other parts of the car — for
example, in the steering gear /x will be considerably higher than
this — about 0'15, and the angle is then a little under 9 degrees ;
but reversibility here is really undesired although usually
obtained. In designing the gear, the determining factor is the
wheel, for if the heel teeth is capable of withstanding the load the
worm thread will be sufficiently strong since the worm is of steel
and the wheel of phoshor bronze, usually. The working that
will subsequently be given will be more in connection with rear
axles, but its application to other worm drives will be readily
seen.

If the torque is T and the velocity ratio is X, the twisting
moment on the wheel shaft is Tx and the ratio of the number
of wheel teeth to the number of threads on worm is x. Let r be
the pitch radius of the worm and R be the radius of pitch circle

of the wheel. Then — is the pressure tangential to the circum-

lead
ference of and at the pitch circle of the worm and ^ — - is the

tangent of the pitch angle d. The thrust along the shaft

neglecting friction is - cot ^ = -;- , — ^ = , — -r and the total

T
normal pressure between the teeth = — cosec 0, Generally, the

worm wheel subtends an arc of 60 degrees with the worm, and hence

the circumferential length at the pitch line will be -^ irr, the true

length of the circumference in contact at the pitch line will be

^ Trr sec 0. The twisting moment on the wheel shaft is Tx, so

Tx
that the tangential force acting at the pitch circle is -|- and this

is equal to tlie thrust along the shaft.

GEARING 291

R r

^ = cot 5
X

But will be determined by considerations of efficiency, and x
is known from the gear ratio required, therefore the value of ^^ is

known.

Now decide upon the number of starts (u) to be used in the wovm,

then aj times this number will be the number of teeth (N) in the

wheel which should not be less than 30. Choose a probable circular

pitch, p, the normal pitch will be p cos and if the worm is to

be cut by diametral or circular pitch cutter, p cos should be

one of the standard sizes. The circumference of the pitch circle

Nn
of wheel = Up and the radius -, -, so that the tangential force

acting at the pitch circle = tj- ^= — —: The normal

pressure on the teeth is therefore (tangential force x sec 0) =

^TT — sec and this is the load which the teeth must be

capable of withstanding. It is well at this stage to check the

lead of the worm, as it is inconvenient to use odd pitches.

Therefore, having estimated the pitch and calculated the radius

V cot
of the wheel, substitute in the equation ^s = and find r.

Then the lead is 27rr tan 0. By slightly varying a suit-
able pitch can be obtained. The number of teeth in contact con-
tinuously is usually two, but there may be three at some times
depending upon the proportions employed. Assuming that two
teeth are in contact, and that the load is equally distributed, the
worst condition is when the load is on the point of the tooth.
If 1 is the height, and h the thickness at the root then : —

2'rrTx sec ^ ^ 1 1 710,.
Nj> 2 (5

All these quantities are either known or have been assumed
excepting the value of h and the stress. The length of the
surface in contact given above at the pitch line of the worm is

u 2

292 MOTOR CAR ENGINEERING

- 7rr sec 6 where r is the pitch diameter of the worm. Fracture

will, however, take place at the root of the tooth, hence the
radius to be considered will be- r + 2 (dedendum) = ?'i. The

value of r = and, therefore, ri= ^ + 2 (dedendum).

X X

By substitution-

8 " """ M X
Hence —

27rTxsec^ ^1 11 /I /^Rcoti^ 1 o 1 ^ ^ ^ ja*'

X - = T. . T TT sec ^ I + 2 dedendum I Ay

ri = -5^ TT sec d \ 1- 2 denendum .

Np 2 6 3

18T j:1

/ =

Npfe^ ( h 2 dedendum]

The stress employed should allow of a factor of safety of at
least 8 to be used, and should the dimensions of the teeth
that were selected not allow of this, the pitch of teeth must be
increased accordingly. Should any alteration be necessary, the
lead of the worm should again be checked to see that it is of a
standard size.

171. But the worm must also be capable of supporting the load
without abrasion. In spur and bevel wheels, although sliding
takes place, the motion is partly rolling ; but in worm wheels the
motion is wholly sliding, and hence a greater amount of heat will
be generated at the teeth. It would therefore be reasonable to
suppose that the permissible pressure is in some measure depen-
dent upon the velocity of the surfaces, and this is borne out by
experiments carried out by investigators. The bearing surface
necessary is probably influenced by the load, the velocity of
rubbing, the condition and nature of the surfaces in contact, the
efficiency of the lubrication and the rate at which the heat
generated is carried away. Hence, the settlement of close limits
of pressure is difficult because of the possible variations in the
above factors, and any quoted must be subject to restrictions on
account of this. Professor Unwin quotes the case of a Hindley
or Lanchester worm that gave good results in which PV =
2,000,000, where P is the end thrust in pounds and V is the
velocity at pitch line in feet per minute, and even higher values

GEARING 2P8

than these were recorded in the American Machinist in 1897.
In automobile practice, for ordinary worms, the value of PV
varies between 750,000 and 1,200,000. Obviously, it is desirable
to use a constant as near to the lower figure as possible. With
the coefficient of friction assumed above, namely, 0*05, it is
interesting to note that the heat units absorbed in friction per
minute are from 4*8 to 7*7 B.T.U.

172. It is most essential that ample provision is made for the
end thrust on the worm, and with large angles of for the wheel
also, as many troubles ensue if this is overlooked. The axial
thrust on the worm is —

,, = - cot 0.
K r

Either of these may be used, and suitable bearings selected for

carrying the load at the maximum speed of rotation. The side

. T
thrust on the wheel is tan 0, and similar precautions must be

adopted in this case.

The pitch diameter of the worm has above beea determined by
considerations of obtaining a definite velocity ratio and a high
efficiency. In some cases, however, where little load is carried,
this is not so, but it is made from IJ to 3^ times the linear pitch
without reference to the efficiency. For rear axle worms the
ratio is generally between 1^ to 2^, but this is of little import-
ance here. The variation indicated above is in some measure
owing to the method of fixing, as when the worm is solid with
the shaft a smaller diameter is possible than when it is keyed or
pinned on to it.

For further remarks re worm axles, see Art. 185.

178. Chain Drives. — In recent years considerable attention has
been directed to the application of chains for driving the cam
and magneto shafts, and for employment in the gearbox, largely,
if not entirely, on account of the silence of this form of drive,
even after long periods of use. In many cases, principally on
commercial vehicles, it is also used for driving the road wheels.
The chain used for this purpose is of the inverted tooth type, and
it is claimed for it that it will run silently and continuously at a
high efficiency, and that the need for accuracy in working is
reduced. And against this that the adjustment of the angular
positions of the cam and crankshafts is not so fine because of the

294 MOTOR CAR ENGINEERING

greater pitch of the teeth that, although from the shape and
action of the tooth and chain any elongation from wear or
stretching in the length of chain round wheels is taken up by the
chain rising up the teeth, it is unable to allow for elongation in
the parts of the chain between the wheels and that it )'» essen-
tially a drive where the load does not fluctuate greatly. These
disadvantages may be largely overcome by the use of means ol
adjustment whereby errors in the relative angular positions of the
shafts may be corrected or minimised. Whether this type of chain

1''IG. 50. — -t'liain ilriven Gearbox.

will eventually supersede spur-wheels in the positions mentioned
or not it is impossible to say, for great advances have been made.
Probably it has a. great future for driving valve mechanisms,
especially of the sleeve, piston and rotary t\ pe, but the difficulty
in fitting three chains that will work well on the same centres,
combined with the rather massive gearbox they entail, would
ai)pear to be serious drawbacks to their extensive use in change
speed gears.

174. Points in the Design of Chain Drives. — The two principal
factors in the design of a chain diive are the speed of the chain
and the load which it has to carry. Means are required to pre-
vent the chain from working endwise and are obtained by the
use of guides built up with the chain. The guides may be in the
centre — in which only one is needed— or on the outside where
two are required. For the former a groove is cut in the wheel

GEARING 295

across the teeth. Messrs. Hans Benold, Ltd., of Manchester,
state that they aim at getting a pressure of from 2,000 to
5,000 lbs. per square inch according to the chain speed, the
bearing pressure being more important than the strength of tlie
chain and fit the following size of chain for cam-shaft drives : —

For engines up to 80 mm. bore— 0*5 in. pitch, 1*2 in. (with
outside guides) ;

For engines between 80 and 90 mm. bore— 0*5 in. pitch,
1*4 inch (with outside guides).

For gearbox drives the f-in. pitch chain may be used, the
width being varied according to the power transmitted, keeping
the requirements as to pressure mentioned above. The bearing
areas are important because excessive loads on the chain cause
high pressures in the rivets, since the wear at the teeth should be
small on account of the fact that little sliding motion takes place
at this point.

Messrs. The Coventry Chain Co., Ltd., recommend J-in. to
|-in. pitch chains for camshafts and from 8-mm. to ^-in.
pitch chains for magneto drives. A chain-driven gearbox fitted
with these makers' chains is shown in Fig. 50, where it will be
observed that the meshing of gears is effected by clutches, while
the reverse is obtained by means of spur wheels. Both the
above firms state that the best results are obtained when the
factor of safety under normal working conditions approximates
to 30, but even a little higher may be necessary under some
circumstances.

It is advisable, in setting out a chain drive of any kind to
avoid the use of a vertical or nearly vertical length of chain, and
where possible the driving side should be at the top in order that
the weight of the chain may assist in releasing the teeth from
the wheels. The pitch of the centres of the shafts should not be
less than one-and-a-half times the diameter of the smallest wheel,
otherwise the angle of contact on the pinion is too small ;
neither should the number of teeth be less than fifteen and prefer-
ably seventeen. The latter can always be arranged for by reduc-
ing the pitch and increasing the width of the chain. Jockey
pulleys, where fitted on the outside of the chain, should be of
fibre to prevent burring over the edges of the chain, but if on the
inside an ordinary chain wheel, which should be of as large
diameter as possible in order to reduce the curvature through

296 MOTOE CAR ENGINEERING

which the chain must pass, which meshes with the teeth of the
chain. Chain wheels should be made as large as practicable so
that the pull on the chain will be minimised, especially if the
load is at all of a fluctuating character.

The maximum speed at which a chain should run should not
be greater than 1,800 ft. per minute and provision should be
made for lubrication. Preferably lower speeds should be
employed, say, not more than 1,500 ft. per minute, as the life of
the chain is thereby lengthened.

In arranging a chain drive, the distance apart of the wheel
centres should be such as will allow an even number of chain
links to be fitted. To assist in this the following formulee
are given which are from Messrs. The Coventry Chain Co.'s
book : —

For xcneqnal wheels.

Chain length in in. = 2L cos ^ + P {~^~ + ^sS^'") "

rxx ' y lu • -i. I. 2L COS ^ , N + n , ^(N — n)

Cham length in pitches = - ^ — -r — t^ — + ^^ — .

For equal wheels.

Chain length in in. = 2L + N P.

Chain length in pitches = -p- + N,

where —

P = pitch of chain in in.

L = distance between centres in in.

N = No. of teeth larger wheel.

n = No. of teeth in pinion.

D = pitch diameter of larger wheel in in.

d = pitch diameter of pinion in in.

= half the angle of wrapping round the

larger wheel minus 90 degrees.

180
The top diameter is P cos -jr--

Pitch diameter is . 180

Readers may refer with advantage to Mr. A. S. Hill's paper
on " Chains for Power Transmission,"

CHAPTER XV

TRANSMISSION GEAR

175. Load on Transmission Gear. — The highest stress to
which the transmission can be subjected is determined by the
load on the driving wheels, the friction between the tyre and the
road and the gear ratios employed ; as if the torque on the rear
axle exceeds a definite amount the tyres will slip. This applies
to cars of any power. The torque on the rear axle is Vfitir
where Wi is the weight supported by the driving wheels, /ut
the coefiBcient of friction between the tyre and the road, and r is
the radius of the wheel. The value of fx will vary with the class
of tyre and the condition of the road surface but may be taken as
0*6 for ordinary purposes ; as a maximum value many designers
use a value of 0*4 ; while Wi and r will vary with the class of
vehicle and the distribution of the load.

The torque on the propeller shaft or cross shaft will depend
upon the gear ratio employed. If x is the gear ratio, since the
torque varies inversely as the number of revolutions, the torque

wUl be -■ — where rj is the mechanical efficiency of the type

TfJU

of gear employed. For vera low powers this will be produced
when braking the vehicle, but if the brakes are only fitted

WiU7'

to the road wheels, then the maximum effect will be — ^—

since the greatest stress will be induced by driving.

For the gearbox shafts, the maximum torque on any shaft

will vary inversely as the number of revolutions. Thus, on the

direct drive the torque will be equal to that found from tho

expression given in the preceding paragraph, but on the indirect,

if y is the ratio of the gear s, and ?/i is the efficiency of a single

pair of wheels - - " is the maximum torque on layshaft.
^ . -nJcy ^ ^

The value of y should be equal to the smallest value of

298 MOTOR CAR ENGINEERING

No. of teeth in wheel on propeller shaft .1 ^i i^ xv

T^T j-r — ;t— :^ r — r^ — f — r— ii — as then the torque on the

No. of teeth in wheel on layshaft ^

lay shaft is greatest. For very high-powered cars it is sometimes

desirable to check for the engine torque, as if the car is rapidly

accelerated, on, say, second speed the extra torque necessary to

produce the angular acceleration of heavy tyres may be sufficient

to cause higher stresses in mechanism than those induced by the

torque given above.

176. Universal Joints. — Contrary to the opinion sometimes
held universal joints are one of the most important parts of the
car, as from their position frequent attention is not often given to
lliem. Consequently, unless carefully designed, there may be
considerable friction losses, because they are continually in action
from the rise and fall of the axle and the normal angularity of the
shafts.

The construction of these members may be seen in Figs. 51, 58,
etc., while others are shown in Vol. I., 110, 119, etc. There are,
however, many forms differing only in detail, but all embody
the principle that the centre about which the fork or coupling
attached to each shaft turns is common to both shafts, and
coincides with the point of intersection of the axes of the two
shafts, and that motion is possible in two planes at right angles
to one another. In the design illustrated in Figs. 55, etc., a
muff in which steel-faced grooves are provided receives a fork
carrying trunnions fitted with bronze bushes. There is thus
a single centre of rotation motion in one plane being allowed
by the bushes sliding along the grooves, and in the other plane
by the rotation of the trunnions about their axis. In Fig. 51
a block is shown which carries two pins pivoting in a casting
attached to the brake drum, while a fork carried by the end of
the propeller shaft pivots about a pin passing through the block.
It will be noted that the pin is bushed. In other cases, two
forks are used, or the end of the propeller shaft is made spherical
and hardened balls fitted thereto, one half of the ball being
within the sphere and the other half slides in a rounded groove
in a muff (Fig. 112, Vol. I.) while instead of balls, keys are
sometimes machined solid with the spherical end.

It is desirable in most cases that axial movement should be
possible, hence, where the design does not allow of this, a sliding
coupling should be provided. This is necessary because the rise

TRANSMISSION GEAR 299

and fall of the shaft may shorten or lengthen the distance between
the axle and the gearbox and, therefore, when the rear axle is so
restrained that it rotates about a point in Hne with the forward
universal joint it would appear that it might be safely omitted,
but it is considered that in all designs such movement should be
possible so as to compensate for initial errors in the distance and
to allow for frame distortion. Such a joint should always be
provided between the engine and gearbox for the reasons just
given.

As regards the number of universals fitted, the two positions
in which they are necessary are in the clutch shaft and in the
propeller shaft. For the former, perhaps one would suffice, but
two are better, since variations in angular velocity are reduced.
For the latter, two are essential for efficient working, although
one only is often fitted but is objected to because of the variatibn
iu the angular velocity of the end shafts and the increased stresses
resulting from the rapid acceleration of the vehicle produced
thereby. Rankine's formulae for the angular velocity of the
shafts attached to any one joint is —

Vi = V cos a

COS a
where V is the angular velocity of the gear or bevel or worm shaft
(in this case)

Vi is the minimum velocity of the propeller shaft (in this

case)
Va is the maximum velocity of the propeller shaft (in this

case)

a is the angle between the axes of the shafts at either

joint.

The condition for uniform angular velocity between the gear

and the bevel shafts is that they must be equally inclined to the

propeller shaft, and this is evident from the above equations.

Now if only one universal joint is used, the bevel shaft must be

inclined to gear shaft and in line with the propeller shaft, and hence

the former will at times endeavour to accelerate the latter very

rapidly, and at others the latter will move faster than the former,

resulting in high loads being thrown on the shaft (since the car

cannot be so rapidly accelerated without excessive stresses being

induced), and if there is any play between the teeth of the wheels

300 MOTOR CAR ENGINEERING

some noise must also be produced. The only relieving factor
will be the elasticity of the metal in the propeller shaft itself.
But if two universal joints are employed the angular velocity of
the two end shafts will be constant and only that of the propeller
shaft will vary, which, on account of its small inertia, will
necessitate but little increase in torque. It will be clear that as
the angularity of the shafts increases, so does also the angular
variation in speed ; and hence it is desirable to reduce the angle
of inclination as much as possible below 16 degrees, which is the
maximum angle at which good results can be anticipated. Engines
are sometimes inclined in order to do this.

177. In the desicfn of universal joints the questions of strength
and of bearing surface must receive attention. For strength it is
suflScient to consider the section of the pins close to the fork, as
generally the fork, or its equivalent in other designs, is of a
sufiBciently robust design to be amply strong to resist the bending
loads which it is called upon to bear. The section is circular, and
if the diameter is J, the radius from the axis of the shaft to the
section considered is r and T is the torque in the shaft — the

shearing force at this point is - which is resisted by two sections

each of —r- area. But as there must be some bending of the pin
only If times the area of one pin will be taken.

T ..TTfP ..

Hence

r='i rf

* I

d = 0-85 V—

where ,/^ is the stress and should allow of a factor of safety of at
least 12 and 15 with harder grades of steel.

Bearing area will, however, generally determine the dimensions
of the part as it is desirable to keep down the overall sizes as far
as possible, for with large and heavy universal joints great care is
necessary in order to prevent vibration and wear resulting from
any unbalanced forces set up by rotation. The bearing length
will be approximately between 1 and 1*5 times the diameter of the
pin in a forked joint, but will vary with the other types. The
force acting at the centre of area of contact of radius vi to produce

TRANSMISSION GEAR 801

the torque T is T and is supported on area (or length in the case

of line contact) of 2A.

T
Then ,^— . = pressure per unit area.

The intensity of pressure varies within wide limits, ^ossibl;
due to the fact that it has been found from experience that wear
takes place very rapidly rn some designs ; partly because of the
nature of the surfaces in contact, or because of an excessive
amount of sliding motion which takes place at the port. It will
usually be satisfactory to use a pressure of, say, from 1,200 to

Fig. 01.— AiTOBtroug-Whitworth Gearbox.

1,500 lbs. per square inch (*84 to I'OS kilos per mm.^), the
lower pressure being used where practicable, although higher
pressures are sometimes employed.

The lubrication of the propeller shaft joints is generally
performed by enclosing the whole of each joint by a leather
cover, as seen in the illustrations, and filling this with grease,
thus affording an ample supply of lubricant and excluding dust.
But it is also desirable to provide passages or grooves for the
entrance of the grease to the bearing areas, especially if pins
are used — otherwise the grease will be pushed away and the
efficiency of ' the lubrication impaired. For clutch shaft
universals it is sufficient — from their more accessible position —

302 MOTOR CAR ENGINEERING

to provide grease cups from which holes may be led to the pins
or the part required to be lubricated ; albeit, these must of
necessity be of small size or balanced, as the centrifugal force
produced 'by them at high speeds may prove objectionable.

It may be remarked here that the practice of placing the front
universal joint of the propeller shaft well within the brake drum,
or within a spherical end to the torque tube, is not considered
desirable ; as, apart from the inaccessibility of the part, the heat
generated during braking must be partly conducted to the joint
and to the grease contained within the casing, aiid may cause
overheating. The advantages accruing from these methods are
in the direction of cleanliness and neatness.

178. Change-speed Gears. — The class of gearing that will be
considered here is that in which the change iS; eflfected either by
sliding the gears along the shafts or by the use of dog clutches.
The descriptive matter relative thereto has been dealt with in
Chapter XVL, Vol. I., the gearbox construction in Art. 129 of
this volume, and the strength of gearing iii ihe preceding chapter,
so that it is unnecessary to discuss these here.

As regards the position of the gearbox it is generally placed
either immediately after the clutch or incorporated in the rear
axle casing — the latter form being used in increasing numbers,
although the former is the more popular at present. One point
advanced in connection with gearboxes on back axles, others are
given in Art. 197, Vol. I., is, that the rear wheels hold the road
better, and undoubtedly this is perfectly true. In high-powered
' cars, tyre wear is caused largely by the scraping action between
the tyre and the road, when the tyre reaches the ground on the
rebound after passing over an elevation or a depression. The
extra mass in the axle casing is said to prevent the wheel from
leaving the road surface so frequently or for so long a period,
hence, tlie time for the acceleration of the mass of the wheel is
less, and the velocity of the tyre will not have been increased by
so much when it again takes up the drives as when the lighter
construction had been employed. But against this is the fact
that the normal tyre wear must be greater because of the larger
unsprung weight, as must also be the blows to which the tyre is
subjected. It would therefore appear to be entirely a matter for
experience to determine, although the result must be largely
influerced by the qualities peculiar to the design considered.

TRANSMISSION GEAR 303

There are two pointa to which particular attention should be
drawn in connection with rear axle gearboxes, namely, that the
roda used for the striking gear should be supported in some way

Fio. 52.— 13-9 ArmatroDg- Whit worth Gearbox.

along their length in order to prevent them whipping with the
vibration o[ the axle, and that the forward ends should pivot
about a point on the same axis as the front universal joint, so
that the lise and tall of the axle will not produce any effect upon

304 MOTOR CAR ENGINEERING

the rods themselves. In order to obtain rigidity it is desirable
to use tubing in lieu of solid rods for this purpose.

The almost universal method employed for changing gears is
by means of the gate change, and rightly so, for the advantages
accruing from its adoption are manifold. The length and weight
of the gearbox are decreased, the shorter shafts from their greater
rigidity conduce to a better tooth action, and the meshing of the
gears is certain, while any gear can be selected at once and the
lever is always in an accessible position.

179. Arrangement and Details of Gearbox. — The general
arrangement of the shafts is for the layshaft to be placed on
the near-side of the primary shaft and the striking gear on the
off-side. This is largely determined by convenience since, as the
driver is seated on the off-side, the actuating gear can be best
arranged on that side, while the position of the layshaft enables
inspection and access to be obtained through tlie cover of the
box, and does away with the necessity for a deep box that would
require an inordinate amount of lubricant.

The sleeves carrying the sliding sleeves are mounted upon the
gearbox portion of the propeller shaft, which is usually provided
either with four or six castellations or keys (see Fig. 53),
or with finer castellations, which give the shaft the appearance
of a long toothed wheel, but in a few instances four key, are
fitted, being secured by screws. When the smaller number of
castellations are adopted they are often simply cut into the shaft
by a milling cutter, so that the sides are parallel throughout
their depth. In most designs (see Figs. 51, 53), the for-
ward gears actuated by the striking fingers are made separately
for convenience in cutting and each pair bolted together before
assembling. For the layshaft gears, these can be cut upon a
sleeve secured to the shaft, or may be bolted to flanges formed
on the shaft itself, but occasionally the smaller diameter wheels
are solid with the shaft, and the larger gears are cut upon a
sleeve attached to the shaft. The construction, employed in
several representative designs are shown in the illustrations
given in this chapter. In a faw cases one of the sliding sleeves
is mounted upon the layshaft, but the other must be in the more
usual position in order to allow of the direct drive to be obtained.
The reverse gears are ordinarily placed below the forward gears,
sometimes at one end, and at others in the centre of the box.

TRANSMISSION GEAR 805

It is eBsealiiil that the engine portion of the divided shnft
should be in correct aligumenb, and hence two bearings are
necessiry. These are generally both placed at the engine end
of the gearbox, but occasionally the engine shaft is extended and
the rear end supported in n ball-bearing within the divided shaft,
which has also a plain bushed bearing at the front end surrounding
the engine sliaft. Where this conBtruction is not employed the
front end of the divided shaft may be run either in plain or small

Fig. o3.— 20-28 h.-p. Armstroug-W bit worth Uearbojc.

ball-bearings, but if the former, careful attention must be given
to the lubrication of the part. Two ball-hearings may also be
used to support the propeller shaft extension. Two ball-bearings
close together are not infrequently used on account of the
necessarily small dimensions employed, but a double ball-bearing
is preferable for this purpose, since the equal distribution of the
load can be better ensured. Ball-bearings, wherever fitted,
should have their inner races secured tightly to the shafts upon
which they are placed, and means for locking the nuts of all
parts must be provided.

The permanent layshaft wheels have, in a few instances,
helical teeth, and ball thrust are then neeeasary on both shafls

1I.C.B. X

306 MOTOB CAR ENGINEERING

They are generally placed at the front end of the box, either
between the two ball-bearings supporting the engine shaft, but
more usually immediately after them. The direct drive may be
obtained by one of these methods. The common method is to fit
dogs on the next speed wheel (either lower or higher according
as the direct is on top or not) which are brought into engagement
with dogs fitted to the engine shaft, or a sleeve attached to or in
one with the constant mesh wheel on that shaft. In the other
two forms, either an internal or an external toothed wheel is
on the engine shaft, sometimes formed in the interior of the
permanent meshing pinion of the former, and either an external
toothed wheel (sometimes the next speed wheel) or an internal
toothed wheel is brought into engagement with it for the direct
drive. These several points are shown in the illustrations in either
this book or Vol. I. The edge of the tooth on which the sliding
and fixed wheels are brought into engagement must be tapered
off slightly so as to facilitate gear changing.

The arrangement of the striking gear offers little scope for the
ingenuity of the designer. The selector lever is usually secured
to a shaft placed above the gears in the upper part of the box,
and the rods (which are two or three in number according as
there are three or four forward speeds) are in the lower portion
of the box. In some designs the sliding fingers move along
these rods which are fixed (see Fig. 54), but in others a rigid
connection is made and the rod and fingers move together
(see Figs. 51, 52, 58). For locking the rods or the fingers
in position several devices are employed. In Fig. 54 an open
framework in the form of a sector is pivoted at the bottom and
the two arms encircle the rods — the method of operation being
quite clear from the illustration. In Fig. 52 another form is
seen, which is of the pendulum type, while a different design is
illustrated. To retain the fingers in the position in which they
are placed by the selector lever and prevent them from sliding
about should there be any play, spring loaded balls or plungers
are employed, which engage in recesses in either the sliding rods
or the fingers. These may be contained ia the casting or in the
fingers, the former being necessary when the rods themselves
slide. The details of the connections between the fingers and
the gear wheels and the striking rods may be seen from the
various illustration^.

TRANSMISSION GEAR 307

180. Number of Speeds and which Direct. — In practice the
number of forward speeds provided are either two, three or four, and
apparently are determined irrespective of the power of the engine,
although the lower the ratio of horse-power to the weight of the
car the more necessary it is to have a larger number of speed
changes. It would be desirable to have a very wide range of
gears, especially in small-power cars, as the engines could then
be run continually at a high efficiency, but because of the increase
in cost of manufacture and in the size of the box accompanying
any increase in the number of gears, it is usual to limit them to
either three or four, although in the case of high-powered cars it
usually* happens that the direct drive is only employed, excepting
when starting from rest or on hills. The necessity for frequent
changes of gears becomes more imperative as the power weight
ratio decreases, since the frequency with which the torque trans-
milted to the driving wheels on any particular gears falls below
that necessary to overcome the resistances offered to the passage
of the car at the speed which that gear represents is greater.
The torque should always be slightly in excess of the power
requirements, otherwise the engine will commence to '*flag" and
eventually slow down. On the other hand, it should be unneces-
sary to race the engine in order to obtain the maximum speed at
which the engine is capable of driving the car, neither should
there be too great a drop of speed between any two gears, and hence
the appropriate selection of gears is of the utmost importance,
especially as one naturally drives on the highest gear as long as
possible in order to economise in the consumption of petrol and
to minimise vibration.

With a four-speed gearbox either the third or the fourth may
be the direct drive, but in a three-speed box it is usual to make
the top gear direct. The choice should, however, be influenced
by the power and weight of the car and the nature of the roads
upon which it is employed, but it would appear more satisfactory
for a low-powered car for service in a hilly district, on rough
roads, or for town use, to make a lower gear than the top the
direct drive — that is, the speed on which the car will be more
frequently employed — then, should the resistances encountered
permit of a higher speed, it may be attained by the use of the
indirect top. Much will, of course, also depend upon the speeds
of the cor represented by the gear ratios, and in most cars

X 2

MOTOK CAR ENGINEERING

TRANSMISSION GEAR a09

manufacturers offer two or three alternative gears — a bigb, low,
or a standard gear. In all cases the drop of speed between direct
and the next below it should be suflBcient to allow for the decrease
in the torque due to the indirect drive.

181. Ghear Ratios. — The gear ratios employed on a car are
principally determined by —

(a) Weight and type of body fitted.

(/>) Power of engine at normal speed of revolution.

(d) Car speed or direct drive.

(e) Diameter of tyres fitted.

If (a), (e) and either (c) or (d) are known, then (b) and either
(d) or (c) may be found, but if the (a) (i), and (e) are fixed (as is
usual) then (c) and (d) must be suitably proportioned, otherwise
the power will be insufficient to do the work if the car is over-
geared or too great if undergeared. The minimum horse-power
of the engine will generally depend upon the speed at which the
maximum gradient is climbed, but if a car is used for racing
purposes the wind resistance will largely influence the power
required. As has been stated in Art. 50, all cars should be
able to ascend a gradient of 1 in 4, and in determining the gears
for the direct drive it should be assumed that the car is climbing
a gradient of (say) 1 in 40 or 1 in 50, as unless this is done it
may be necessary to change down immediately any little incline
is reached, or if the conditions are in any way unfavourable,
such as with a head wind or a little extra load, or if the engine
is not in perfect condition. It will be clear that the car speed at
normal revolutions on the direct drive will be only influenced by
the gearing in the back axle and the size of tyres fitted, but the
power required will depend solely on the car's speed and weight
and the gradient and wind resistances.

The methods of working where (a) and (c) are given and (b) has

to be found or where (a) and {b) are known and (rf) is required

are shown in the example Art. 50, but in these the gear ratios are not

referred to. It is clear, however, that if the speed of the car on the

direct is 29*4 miles per hour and on the low gear 7 miles per hour,

29*4
the gearbox ratio must be —;=— = 4*2 to 1. Further, a speed of

310 MOTOR CAR ENGINEERING

29*4 miles per hour on direct driv<3 is wpt^ feet per

minute, therefore, if. the tyres are 810 mm. diameter, and the

normal engine speed is 1,200 revolutions per minute, the gear

. . . , , , .„ , 1,200 X 60 X TT X 810 oorj ^u 4r

ratio HI back axle will be ^-7^1 ^-p^^k — -T7i — nr^A = 3*87 that

29-4 X 5,280 X 12 X 254

is (say) a 16-tooth pinion and 62-tooth crown wheel. Such a
car, if the engine can be accelerated to 2,000 revolutions per
minute would be able to travel at a speed of 49 miles per hour,
and at 2,500 revolutions per minute at 61*2 miles per hour should
the resistances be suflBciently low. If the engine torque is practi-
cally constant over the range of speeds mentioned the brake
horse-power developed at those speeds would amount to about
84*2 and 42*8 respectively.

182. A more general procedure is to work from the torque
considerations as is outlined below. The tractive effort (F)
multiplied by the radius (R) of the road wheels is the torque
required on the live axle shaft to overcome the resistances to
the car's motion. The engine torque (T^) multiplied successively
by the gear ratio (x) and the efficiency of the transmission (e)
gives tlie torque on the live axle from the engine. Equating

these —

FR= T, X X X e.

Now the value of F =/. +/^ -\-f^ where /r,/^,,/^ are the resist-
ances offered by the road, gradient and wind respectively. But
/,. = road resistance multiplied by weight of car,/, = weight of
car (?r) divided by the gradient (d) and /^ = fcV^A = the force
obtained from the accelerometer readings as required to overcome
the wind resistance at the car speed considered. If a series of
accelerometer readings are not available, the constant k may be
determined from existing cars, or may be estimated from known
results, such as those in Arts. 50 to 52 and A is the assumed
projected area of the car.

As has been stated in Art. 49, the road resistance may be
taken as 70 lbs. per ton (0*03125 kilo per kilo) while the
gradients which it., is required that the car should climb are
known. The probable weight of the car, the size of tyres and
the transmission efficiency may be assumed and the engine
torque can be calculated, so that by substitution in the equation
civen above the value of x can be calculated. If F and R are in

TRANSMISSION GEAR 811

lbs. and inches, then T^ will be in lbs. inches, but if in kilos
and mm., T^ will be in kilos mm.

Example. — If the weight of the car (fully loaded) is 2,500 lbs.,
the wind resistance equal to a force 0*05 V^, the engine torque is
1,000 lbs. ins. at normal revolutions and 810 mm. tyres are to
be fitted.

,p, . 2,500 ^ ^^ r,o IV r 1 2,500 _

Then f, = ^^ x 70 = 78 lbs., f„ on low gear = '^ =

625 lbs., and "'|^ = 62*5 lbs. on top gear,/, = 0*05 V and

405
(78 + 625 + 0-05 V^) g^ = 1,000 X x X 072 for low gear,

and (78 + 62-5 + 0-05 VJ) -^ = 1,000 X ^ X 075 for direct

Zt) 4

gear.

On account of its low magnitude the resistance due to the
velocity of the car is negligible on bottom gear.
Hence —

703 X 405 _
25-4 " ^^^'
X = 15-6.

For the direct drive — Vi = rr^-. — , ^^ o^»n and it is now

25*4 X 63,3b0a:i

necessary to assume a numerical value for Vi or for n (the

number of engine revolutions per minute). If n is 1,250 revolu-

.. • ^ TT 27r X 405 X 1,200 114

tions per mmute Vi = , ^^ , ,.,' ,,^^ = — .

^ xi X 25-4 X 63,360 xi

Therefore (l40 + 0*05 {-^) *) |^ = 750j-i

750 x] - 2,230 xi — 10,350 =

.r = 3-89.

This is the ratio of bevels in rear axle, and since the total gear
ratio on low gear is 15*6, the maximum gearbox ratio will be
4*0, the speed of car on top gear 29*4 miles per hour, and on-
bottom gear 7'35 miles per hour.

Having obtained the top and bottom gears the intermediate
may be found in two ways — either by arranging them in
geometrical progression, which gives very good results, or by
assuming that the car will ascend a certain gradient of (say)
1 in 10 for the second speed and 1 in 20 for the third for a four-

312 MOTOR CAR ENGINEERING

speed gearbox, and (say) 1 in 15 for a three-speed gearbox.
The working will be similar to that which has just been shown to
find Vi if the latter method is adopted — the gear ratio obtained
will include the rear axle gears, so that to find the ratio of the
gears in gearbox the result must be divided by the back axle ratio.

If the former method is employed, the geometric series is
a -\- ar '\' ai^ + a/*^ + . . . . for a four-speed box

and a -\- ar + at^ -\- for a three-speed box,

the first and last terms being the bottom and top gears and r
the ratio between two adjacent gears. In the example worked
above for a four-speed box, a is 4*0 and at^ is 1. If the direct
is on the third speed, the third term would be 1.

Since a = 4 and ai^ = I

i^ = 0-25
r = 0-68

Hence a = 4, ar = 2*52, ar^ = 1*585 and ar^ = 1, the corre-
sponding speeds being 7*35, 11*65, 18*5 and 29*4 miles per hour
at normal engine revolutions.

Having decided upon the ratio of the wheels in the per-
manent layshaft drive, the ratios of the speed gears may be
determined.

Some small adjustment of the ratios will be required in order
to obtain suitable pairs of wheels to gear together when placed
in the shafts parallel to each other, and may necessitate the
alteration of the ratio of the constant meshing wheels.

188. Gear Shafts. — These, as has been previously stated, are
usually fitted with either four or six castellations or splines, gene-
rally solid with the shaft, but occasionally where four keys are
employed are separate therefrom and secured in place by screws.
Toothed shafts may also be used. The use of separate keys is,
however, undesirable, as apart from the tendency they have to work
loose in their seats, there is always some risk that the screws may
fall out. In the fine toothed form the teeth are rather more liable
to become distorted than in the commoner type, and hence produce
jambing. Furthermore, fitting the wheel on the shaft so that
all the serrations take up the drive without undue play between
the parts is a somewhat difficult matter. Square shafts are
to be avoided, as they soon become ill-fitting and have tiie
tendency to burst the wheel.

Gear shafts must be considered in design from the aspects

TRANSMISSION OEM!

314 MOTOR CAR ENGINEERING

of strength and angular distortion under torsional stress and
deflection from the thrust between the teeth, which would cause
bad tooth action. The latter is, however, usually unimportant
when the torsional conditions are satisfied with the short shafts
that are now employed, since the load is distributed by the
sleeves for some distance along the shafts. To ensure longevity
of the wearing surfaces, it is necessary for them to be hardened
either direct or by casing ; hut preferably by the latter method,
since gear shafts are subjected to exceedingly heavy and sudden
shocks in service and the elastic core obtained in case-
hardened material is a great advantage in this respect, while
the hardened exterior assists in resisting the distortion of the
shaft.

It is necessary, in order to avoid excessive friction between
the sleeves and the shaft, to reduce the angle of torsion as far
as possible, and this object may be achieved in three ways,
by using a large diameter, that is, by reducing the stress, by
using a material having a low percentage elongation, and by
keeping the sleeves as short as possible. The latter is determined
by the movement that must be given to the wheels to put them
in and out of mesh, and is always kept at its minimum value
in order to prevent excess deflection accompanying long shafts,
as well as to enable a small gearbox to be used. A low
elongation is undesirable, since the capacity of the material
to absorb shock is diminished and hence a low stress must
be employed — the factor of safety ranging from 10 to 15.

Hence twisting moment = 777^],^'^

where/, is the stress and d is the minimum diameter of the
shaft, Le,, at the bottom of the key ways. The determination of
the angle of torsion of the shaft when subject to this stress
would be possible with a homogeneous material, but as the
conditions of loading and the resistance of the material are
somewhat obscure, it can only be accurately obtained by
experiment. The keys may be proportioned according to the
ordinary rules for such parts, but often a uniform depth is
used for all shafts and the number of castellations varied with
the size of shaft employed. It will be found that the keys are
amply strong to resist the shear, but this is required in order to
limit the intensity of pressure and reduce wear.

TRANSMISSION GEAR 815

When the twisting moment is transmitted through the
sleeves, the equation will be

Twisting moment = ^ /* ( p "^ )

where D and d are respectively the external and internal
diameters. It should be remembered that the relation between the
twisting m.oment8 on any two shafts is inversely as the number
of revolutions they make per minute.

For the diameter of the bolts securing a wheel to the sleeve —
let n be the number of bolts and r the radius at which they are
placed. Then the force acting at radius r

= ^. and the shearing force taken by each bolt

_ Twisting moment

nx radius * .

Therefore Twisting moment ^ ^

nx radius 4

where S = diameter of bolt.

184. Propeller Shafts. — These are designed for torsional stress
and checked in order to ensure that at high revolutions there
will be no whirling. The greatest twisting moment on the shaft
from the engine occurs when the car is on the lowest gear, but
this is limited by the load, upon the driving wheels plus the
torque required to produce the acceleration of the road wheels,
etc. (See Art. 151). When the gear and bevel pinion shafts are
not parallel, these may be augmented by a not inconsiderable
amount due to the attempted acceleration of the car with the
variations in the speed of the bevel shaft.

Then if T^ is the twisting moment —

T, = ^^ M'

where d is the diameter of the shaft. The stress should allow
of a factor of safety of eight at least to be employed.

But since the material of which the shaft is composed is not
perfectly homogeneous, and the weight of the shaft itself will
cause some deflection, the centre of gravity will not always
coincide with the axis of rotation and vibration may aggravate
this eccentric loading ; hence, as the shaft rotates a centrifugal
force will be set up tending to cause failure through the bending
action introduced. This tendency will obviously increase with

316 MOTOR CAR ENGINEERING

the length unsupported, and as the square of the speed, so that
with the high speeds of rotation now employed, although the
stress produced by the torque transmitted may be quite
satisfactory, the diameter must be checked to ensure that
whirling will not take place at the maximum car speed. It
is preferable that the revolutions should be much below the
critical speed, for the straining action on the shaft combined
with the vibration fiom the rise and fall of the axle and
variations in torque will undoubtedly set up a form of " whip '*
that must be extremely distressing.

For a shaft unrestrained at the ends, such as the propeller
shaft, Professor Morley^ shows that the speed at which whirling
will take place may be found from the expression —

til2 ^ W

where n = number oE revolutions par second, 1 is the length in
inches, g is the acceleration due to gravity in inches per second,
E is the modulus of elasticity, I the moment of inertia of the
section and w is the weight of unit length of the shaft.

Taking the case of a circular shaft 1 J in. diametei* and 4 ft. long

__ TT . / 32-2 X 12 X BO X 10" X ird^ X 4
^ " 2I2 ^ 0-2B X ir(P X 64

_ 80,000 d

^ _ 4,800,000 d

_4, 800,000 X Ij

~ 48 X 48
= 2,600 revs, per minute.

Probably a speed of 2,000 revolutions per minute would be
sufficient to produce marked effects upon the shaft. A shaft
may be considered as freely supported even when resting in
bearings should such be of short length, especially in ball-
bearings.

185. Bevel and Worm Drives. — The procedure in designing
bevel and worm gearing has been dealt with in Arts. 165,
and 168, while attention has been drawn to various points in
connection with these two forms of drive in Vol. I.

» See Morley's " Strength of Materials."

TRANSMISSION GEAR 817

These gears are almost universally carried in ball-bearings,
thrust bearings being fitted to take the reaction between the
teetli. Two sets o( thrust bearings are necessary on the worm.

and one each side for the wormwlieel, in llie case of worm
drives in some cases the thrust for wormshaft are both on the
same side, hut one set only on the pinion &ui another set bt

818 MOTOR CAR ENGINEERING

the back of the crown wheel will suffice for bevel gears, although
two sets are desirable in order to keep the wheels in their correct
position with a minimum frictional loss, and the friction at
the universal joints will produce a thrust in both directions.
In order that the aUgnment of the pinion shaft may be retained
(and this is essential for efficient and quiet operation) two
bearings as far apart as can be conveniently arranged should
be provided, but one will be sufficient for the crown wheel since
the other end of the rear axle shaft is supported near the road
wheel. In some designs an additional bearing has been
provided on an extension of the propeller shaft, and is excellent
because it contributes to the rigidity of the, gear. It is probable
that such a construction would allow of the use of a single
bearing at the back of the pinion, as is usual in such cases,
without detriment.

The necessity for rigidity in both forms of gear is emphasized
in order that correct tooth action may be secured, and this is
especially so with worm drives. Hence, the bearings carrying
the axle-shafts are best supported in housings brought out from
the portion of the differential case in which the pinion is placed
and well ribbed to stiffen them. Generally, these are made
solid, but the splitting of the part in halves and providing caps
to the rear half assist materially in rendering the gear more
accessible for dismantling. Provision is often available for
adjusting the position of the thrust bearing for taking up
any wear, but such is also necessary for the pinion if the
best results are to be secured, although it is a distinct advantage
as regards silence to arrange for such a fitting in either position.
In worm drives the bearings taking the radial load should
be brought as close up to the worm and wheel as possible to
reduce the flexure of the shaft when driving, since bad tooth
action would be thereby introduced ; and the worm shaft should
be made amply large with a similar object in view as well as
because any deflection of the shaft must be ultimately trans-
mitted to the ball-bearings at the ends. This also applies to
bevel gears, although in this case it is for the purpose of
reducing the bending moment on the section at the bearings ;
and since the exact determination of the bending load is some-
what obscure, the shafts should be increased by about 0'125 in.
(3 mm.) in diameter above that required for torque alone. To

TRANSMISSION GEAR 819

prevent the lubricant from leaking along the pinion on worm
shaft, a gland should always be provided.

186. The loads carried by the bearii^s are in the main due to
the reaction at the teeth.

In a bevel gear, if F is the force acting tangential to and
at the middle of the pitch surface producing the torque, then the
vertical load on bearings of both wheels is F. This force F, resolved
in a horizontal direction normal to the pitch surfaces and normal
to the teeth surfaces, in contact will give components of F tan a
and F cosec a where a is the angle of obliquity, while F tan a
if resolved in the two directions at right angles to and along the
axes of the wheels will produce forces of

At the pinion, a horizontal side thrust of F tan a cos <^

a horizontal end thrust of F tan a sin </»

At the crown wheel, a horizontal side thrust of F tan a sin

a horizontal end thrust of F tan a cos <^
where 4> is the angle between the pitch surfaces of the pinion and
its axis.

For worm gears the axial thrust on worm is F, and on the wheel
F cot 6, where F is the force acting tangential to the pitch
line of the worm wheel at right angles the axis of the rear axle
producing the torque on the shaft, and 6 is the pitch angle of the
worm. The thrust tending to separate the worm and wheel
teeth is F tan a where a is the angle of obliquity. The bearings
must accordingly be selected so as to be of sufficient size to carry
the highest loads at the highest speed, without possibility of
failure, and where ball-or-roUer bearings are employed should be
taken from the list of a reliable maker of such parts.

187. The worm shaft is subjected to both bending and torsion.
The torque on the shaft is T = Yr cot where r is the radius of
the worm, F is the force acting at pitch line of worm-wheel,
and 6 is the pitch angle of the worm. The force producing
bending is F tan a (see above), and may be considered as being
applied at the centre of the shaft between the bearings, which, as
stated previously, should be placed as close together as possible.

The reaction at each bearing will be ^ — and the bending

moment at a section close to the end of the worm thread, distant

X from the centre of the bearing, will be ^ . Then

MOTOR CAR ENGINEERING

TRANSMISSION GEAR 321

knowing the magnitude of the twisting and bending moments
on the shaft, by substitution in the formula (see Art. 106) the
equivalent bending moment may be found, and hence the diameter
of the shaft at this section determined. For any other portion of
the shaft a. similar procedure may be employed, and if it is
subjected to a twisting moment only, by equating this to the
resistance of a circular shaft to torsional stress, the necessary
proportions may be ascertained.

As has been previously stated, the bending moment on the
bevel gear shafts near the junction with the wheel is not very
clear, so the diameters obtained from considering them as under
pure torsion only will require to be increased slightly to allow
for this.

The diameters obtained are those at the bottoms of the key ways,
.and the shafts must be thickened up by an amount equal to twice
the depth to which the keys are recessed. If coned ends are
formed on the shafts the dimensions apply to the section midway
along the lengths of the cones.

Two methods of mounting the worm are in Figs. 55 and 57 one
of which shows an overhead drive, while in the other the worm is
placed beneath the axle. With the former the road clearance is
slightly increased and a straighter drive obtained without unduly
inclining the engine or dropping the engine too far below the
framing, although the effect of the latter is beneficial by giving
a lower centre of gravity to the chassis. With regard to the
effectiveness of lubrication, when the worm is beneath the wheel
it is bathed in oil, whereas, if above, it must rely on the oil
carried round by the teeth, but in the majority of cars it will be
found that the acceleration is not so rapid with worm drives as
with bevel drives, probably due to the oil being more or less
expelled from between the teeth in both positions. The advantage
will, however, probably be on the side of the underneath worm,
as then fluid contact is made between the worm and its casing
through the oil bath, and hence the heat generated by friction will
be more rapidly dissipated to the atmosphere thereby maintaining
the viscosity of the oil.

188. Differential. — The differential is fitted to enable the rear or
driving wheels of the car to revolve independently, so that when
the car is turning both wheels will roll upon the ground — the
inner road wheel slows down and the outer speeds up. Two

M.C.B. Y

322 MOTOR CAR ENGINEERING

forms employed are shown in Figs. 56 and 57, the former having
bevel gear wheels, and the latter spur, or face gears. The wheels,
it will be seen, are carried either in a casing or upon a framework
secured to the crown or the worm wheel is free to revolve about
the axle shafts.

In the bevel gear differential two wheels are mounted upon the
ends of the two axle shafts and are in medh with two, three or
four other bevels carried on pins by the casing. In the spur
gear form the small wheels connecting the wheels on the axles
are arranged in pairs on opposite sides of the axis of the shafts
(see Fig. 55) being one pinion on each side in mesh with each
spur wheel, and the two pinions on each side are in mesh with each
other in order that they may fulfil the purpose for which the gear
is intended. The bevel type of gear is more used than the face
gear on account of the larger dimensions that can be given to the
wheels attached to the axle shafts, as by so doing a stronger
design is obtained, since the pitch diameter of the bevels may be
practically as large as the overall dimensions of the pinion and
spurs of a face gear. On the other hand, the correct contact of
spur gears teeth is more probable than in bevels — hence the load
is better distributed. Care is necessary in arranging the pinions
to see that the direction of rotation is correct.

The method of attachment of wheels to the axle shafts varies —
cones, splined ends and squared ends being used. Frequently,
there is a rigid connection, but in some designs arrangements are
made so that it is possible to immediately withdraw the shafts
through the ends. The differential gear can also sometimes be
dismounted entire so soon as the axles are withdrawn.

The load upon the gear is the full torque transmitted, since the
torque on the rear axle is taken through the differential. The
number of teeth in mesh will be the same as the number of bevel
pinions employed, or one-half of the number of spur pinions, as
on account of the small numbers of teeth in these wheels, and the
difficulty of ensuring contact at all wheels, it is unsafe to consider
that more than one tooth in each wheel as in meshl The pins
upon which these wheels revolve are subject to shear, and the
force applied is the torque on the shaft divided by the radius to
the section considered multiplied by the number of bevels for a
bevel gear, and the torque divided by the radius to the section
considered multiplied by 1} times. the number of pinions in mesh

TRANSMISSION GEAR 328

for a spur gear, since in -the latter case there are two sections
subject to shear but possible bendmg will increase the stress in
the part.

It is advisable to bush these wheels in order to maintain the
centres, although their speed of revolution, and the work they have
to perform, is not large.

The proportions given to tlie casing or framing in which these
wheels are mounted must to a large extent be determined by the
ideas of the designer on account of the complex and diverse
straining actions to which it is subjected and the great need for
rigidity ; hence, no rule based on strength considerations alone
can been given for the part.

189. Live Axles. — At one time it was customary to support the
road wheels upon the axles, which were in turn carried by the
axle casing, but at the present day in the majority of cars, they
are mounted on ball-bearings placed on the outside of the axle
casing — the drive being taken up by means of splines or keys or
dogs. This removes all stress from the shafts, except that due to
torsion, and hence it is only necessary to equate the maximum
torque on the shafts to the moment of resistance to find the
necessary diameter. The maximum torque is the weight sup-
ported by any one wheel multiplied by the coefficient of friction
between the tyre and the road and the radius of the wheels.

Therefore —

and /, should be such that a factor of safety of (say) at least 8 is
employed. The value of m may be assumed to be 0*45. •

In some cases, however, there is in addition a bending moment
on the end of the shaft due to the method of support. The
magnitude of this is the product of the weight resting on that
axle and the distance between the centre line of the wheel to the sec-
tion at the edge of the bearing, whence, by substitution of the values
of the actual bending and twisting moments in the formula for
the equivalent bending moment, the latter can be ascertained and
the shaft designed to withstand this load. This also appTies to
the cross shafts of chain-driven cars except where the chain-wheel
is dished inwards su&ciently to bring the centre line of the chain
in line with the edge of the bearing. The bending moment in
this case is the maximum pull on the chain multiplied by the

Y 2

324 MOTOR CAR ENGINEERING

distance from the centre of the chain to the edge of the bearing,
and a similar procedure may be followed in determining the
dimensions required for that part.

The manner in which the connection is made between the axle
shaft and the wheel is clearly exhibited in the accompanying
illustrations as well as those in Vol. I.

190. Axle Casings. — The material used for the axle casing
depends somewhat upon the construction employed. In general,
the aim of some designers is to remove all irregularities on the
exterior as far as possible, so that a smooth surface is presented.
This conduces to cleanliness because not only are there few places
into which dirt may lodge but washing down is facilitated. On
the other hand, a great point is sometimes made of ready access
to every part, for which reason the casing is split in halves for the
full length and in a vertical plane, so as to afford the necessary
rigidity. The casing in such designs is entirely of malleable or
cast iron, and the two extreme end portions carrying the braking
gear, springs, etc., are made separate from the main casting. (See
Fig. 55, Vol. I.)

The material that is perhaps most commonly employed is
piessed steel (in which case the simplest design possible should
be devised), either entirely or with a differential casing also of
pressed steel or malleable or cast iron, cast steel or aluminium.
Much depends upon the details of the design as to whether a
pressed steel centre is possible or not. In one or two designs
the casing is of forged steel. Mention muat be made of
the axle where the gearbox is embodied in the differential casing
— in which case it is almost imperative that at least the centre
portion should be a casting.

When pressed steel is employed, it is usual to cone the tubes,
so as to give great strength at the centre, where they join the
differential casing. The method of attachment of these parts is
important, and a flange should be formed on the cones so that
the bolts used are in tension in preference to placing rivets or
bolts radially, as they are then subject to shear, and it is a
difficult matter to prevent some little elongation of the holes in
course of time which will allow the axle to sag in the centre and
jamb the teeth of the differential. Brake supporting gear and
spring pads may be added to the casing by clamping, or by
casting separate sleeves which carry these parts, and pass over

TRANSMISSION GEAR 325

the outside of the pressed tubes, being retained in position by
riveting, brazing, etc. Since the road wheels are usually over
the outside of the axle casing, it is necessary to keep down the
dimensions as far as possible at these positions, to allow of the
employment of large ball- or roller-bearings without necessitating
unduly large hubs. The tubular axle casing is occasionally seen
in some small and medium powered cars, when because of the
small contact surface at the centre it is essential to employ a tie
rod beneath the axle. It is, however, desirable to fit a tie rod in
all cases where an aluminium centre is used, on account of the
permanent set with alloys of this metal. In cast metal axle
casings, whether of malleable or cast iron, the end portions
carrying the spring pads, etc., should preferably be separate from
the main casting, or else the part to which the wheels are
attached should be of steel, rigidly secured to the main casing,
as it is imperative that there should be absolute freedom from
defective metal in any part of the casing.

Tie rods, where considered necessary, should be provided with
some means of adjustment, otherwise dependence must be made
upon the original setting for correct axle alignment, and it is
well known that steel rod itself sometimes elongates under the
load carried. The objection to such means is that any adjustment
should be made only by a qualified person, as it is quite an easy
matter to nullify the advantages accruing from the device unless
care is taken in making the adjustment. The lubricants employed
in the casing are grease and oil. With bevel drives a mixture of
oil and grease will give good service, but in worm drives oil is
essential. Grease cups are sufficient at the hubs, as it is only
necessary to keep the balls or rollers in a greasy condition.
Where oil is used steps should be taken to prevent it from flowing
along the shaft, as it may then issue from the casings at the
ends, diminishing the quantity of lubricant in the differential
and causing the wheels to become unsightly, and diminishing the
power of the brakes. Ample sized holes should be provided for
the insertion of the lubricant, and a plug should be fitted in the
lowest portion of the casing for the extraction of the same when
any dismantlement becomes necessary. The ball- or roller-
bearings at the hubs should be placed as far apart as convenient,
so that any effects produced by a sideload on the wheels, as when
skidding, may be minimised.

826 MOTOR CAR ENGINEERING

191. Loads on Axle Casing. — The loads on the axle casing is
very complex, and their effects a matter for speculation, so that
any consideration from the aspects of strength must be very
hazy. Furthermore, on account of the obscurity of the allowance
to be made for the methods of fixing the parts together, and 'the
construction necessarily employed, the exact distribution of stress
in the material is practically indeterminate.

In the first place, an axle casing is a beam supported at the
ends carrying loads at the spring pads equal to the proportion of
the weight of the car on the springs at the rear, and a uniformly
distributed load due to the weight of the axle and its attach-
ments. These will induce a tensile stress in the bottom of the
casing, and a compressive stress in the upper portion of the
casing. If a tie rod is employed, the casing may be regarded as
in compression, and the tie rod in tension. In addition, there is
the load due to the torque transmitted during braking and in
driving, which if a torque rod or its equivalent be fitted at or near
the centre of the chassis will be limited to the central portion,
but which if placed at the sides will be taken for the full length
of the casing. There are also local stresses induced by the
reactions at the gear teeth, and at the bearings, and by the braking
forces. To take account of all tliese would be laborious if not
impossible, hence the dimensions given must be such as are
considered suitable, having regard to those which previous
experience in similar or somewhat similarly loaded axles has been
proved to be satisfactory. As a general rule pressed steel tubes
and parts vary little from 5 mm. in thickness, but cast metal
parts should never be made less than this, preferably slightly
thicker to ensure the free flow of metal through the mould. It
will be clearly desirable to keep down the ^weight of the axle
casing to a minimum, as it is a dead weight upon the tyres — not
spring supported — and in this the use of a tie rod is of some
assistance. Should a worm drive be employed, it is of the utmost
importance to obtain as rigid a construction as possible on
account of its sensitiveness to bad alignment.

192. Cones, Keys, and Feathers.— Cones are formed upon ends
of shafts for the receipt of gear wheels, etc., in order to ensure
that the axis of rotation and the axis of the wheel will coincide.
If a parallel end is used there is some difficulty in obtaining a
perfect fit without the use of a slight taper, and especially is this

TRANSMISSION GEAR 327

so in all excepting circular sections, for the wheel rides up on
the key and takes up any slackness which may be present. But
small tapers have the disadvantage that the parts have a tendency
to seize up and render the withdrawal of the shaft somewhat
troublesome, hence the taper employed should be such as will
prevent jambing. It will generally be found that a taper of
from 1 in 6 to 1 in 8 measured on the diameter will give satis-
factory results. The diameters of shafts required to transmit
the torque should be taken to be that at the bottom of the key way
at the middle of the length of the cone, and a small shoulder
should be formed just beyond the end of the cone, so that when
the wheel is in position and screwed home, it will he just clear of
the collar.

For the small diameter shafts used in automobile construction
the proportions of keys and feathers may be found from the
following : —

For keys — Breadth = h=: 0-25 D + 0*05 = 0*25 S + 1.

Deptli =zd =0-125D+ 0-05 =0-1258+ 1.

For feathers — Breadth = ^; = 0*2 D + 0-05 = 0*2 8+1.

Depth = rf = 0-15 D + 0-05 = 0*15 S + 1 ;
where D and 8 are the diameters of the shafts in inches and
millimetres respectively. The keys and feathers should be
recessed into the shaft by an amount equal to half the depth of
the key or feather, so that the overall diameter will be equal to
(D + d) and the core diameter equal to (D — d).

Keys and feathers should also be checked for strength to resist
shear. Knowing the torque upon the shaft, the resistance to
shear is the area of the key at a radius equal to the semi-
diameter of shaft. If 1 is the length of the key and T is the
twisting moment —

1 X h X ^ X /a = resistance to shear.

Therefore-

- _2T

It will be found that so long as the length is not less than
1^ times the diameter for keys, and twice the diameter for
feathers, there will be sufficient strength. If so large a length
cannot be arranged for, it is preferable to increase the number of
keys or feathers than to increase the width.

CHAPTER XVI

FRAMES, AXLES AND SPRINGS — TORQUE AND RADIUS RODS

198. Frame ConBtruction. — The essence of frame construction is
strength and rigidity combined with lightness — strength to
withstand the stresses induced by the load carried and produced
by the flexure resulting from irregularities in the road surface,
etc. ; rigidity in order to prevent the magnitude of the strains
from being such as would cause disturbance of the alignment of
the shafting, excessive friction at the bearings, and undue
distortion of the body ; and lightness, so that the weight
supported and the magnitude of the blows on the tyres, axles,
etc., may not be unnecessarily high.

The attainment of these features is, however, not easy, since
the directions in which the forces are applied are not the same,
neither are they of a like nature, while reliance on the body, the
crankcase or the gearbox for sufficient strength or rigidity is not
to be countenanced for one moment. Therefore, if a section is
chosen such that it is the most economical of weight in one
direction, it will not be the best for resisting forces acting in
another direction, and the section most suitable for bending
stresses offers little resistance to torsional stress. Hence, it is
usual to employ a pressed steel channel girder for the side
frames (tubular and wood-filled box steel frames are sometimes
used for smaller cars), and to fit cross girders, tie rods, gussets or
channel irons to give the requisite support where the straining
actions are greatest. Bigidity is assisted by allowing a rather
higher factor of safety than the nature of the stresses alone
warrants, although this is at the expense of some additional
weight. The pressed steel side frames are more economical than
the other two forms mentioned, since they can be readily tapered
and shaped as may be desirable or convenient near the ends, and
the attachment of the cross frames is not difficult ; albeit they are
less suited for torsional stresses. Tubular frames have the great
disadvantage that bracing and the attachment of various parts

FRAMES, AXLES AND SPRINGS 329

necessitate a great increase in weight. In some chassis the side
members are supported in a vertical plane by means of tie rods
placed beneath them somewhat as seen in the case of rear axles,
but there appears to be little advantage in so doing if pressed
steel frames are employed as then the whole section of the friame
is placed in compression.

194. The Principal Loads to which the chassis frame is subjected,
other than the supported mass, are as follow : When one wheel
of the car passes over an obstacle on the road ; one corner of the
frame is raised and the opposite corner depressed, the whole
tilting about the other two corners if the frame itself is rigid.
This tends to twist one side member relative to the other, and to
resist this several methods are employed :

(a) A tubular cross girder is fitted between the centre and the

rear of the chassis — sometimes two are provided, one of
which may form the rear cross girder. (See Figs. 181
and 185, Vol. I.)

(b) Two channel or cross girders are placed at some distance

apart with the flanges facing each other and are tied
together by two tension rods fitted diagonally. (See Fig.
183, Vol. I.)

ample webbing on its upper and lower surface where it

joins up with the side frames ; or, two diagonal struts are

fitted connecting the centre of the cross girder with the

side frames. (See Fig. 1, Vol. I.)

In the case of the front springs, these are usually placed in a

position directly beneath the frame, and hence only transmit

vertical forces ; but the rear springs, being attached to pivots

carried out from the side members will tend to twist each side

member, the magnitude of the twisting moment depending upon

the extent to which they overhang. If the amount of overhang

is small (and it should be reduced as far as possible so as to

reduce the load on the axle casing by bringing the spring pads

nearer to the wheels), it is probable that the stress induced is not

of sufficient magnitude to need special provision for ; but if large,

it can be met by fitting a cross girder in the wake of the spring

attachments, or by placing diagonal girders between the side

frames and the extreme rear cross girder, or by webbing up the

rear corners of the frame. These latter will also be needed to

330 MOTOR CAR ENGINEERING

resist the racking tendency to buckle the frame in a horizontal
plane should the resistance encountered by one driving wheel be
greater than at the other, or the braking effects be dissimilar,
and will apply whether a cross spring is employed or not, as they
may then also have to strengthen the rear cross member, from
which the support is taken to the centre of the cross spring,
against the torsional stress upon it. Where the attachment
between the frame and the cross spring is through the medium
of a forged steel extension from the side frames the fitting of
such parts may be dispensed with. A tubular rear member will
be sufficient when » rear cross spring is fitted and should then be
carried by special forgings riveted to the side frames. The dumb-
irons to the rear end of the rear springs are usually secured to
the frame by a right-angled attachment, one side of which is
riveted to the side frame and the other side to the cross member ;
but such construction is rather for the purpose of strengthening
the means of attachment, for the cross member at the extreme
rear is ample to prevent any distortion taking place from this
cause. An extension of the side frames beyond the rear cross
member will enable the dumb irons to be dispensed with, but this
is a somewhat inferior design, on account of the difficulty in
providing against torque effects.

Then a support must be provided for the attachment of the end
of the torque rod. This may be taken at or near the centre of a
cross girder, or in cases where the torque rods also serve the
purpose of radius rods the end may be carried by a bracket
brought out from the side frames. Its position should be
determined by the front universal joint in the propeller shaft, as
the propeller shaft and the torque rod should hinge about the
same axis.

The supports necessary for the gearbox and engine will depend
entirely upon the system of suspension employed. With an
under frame, a cross member, either of channel, U, or of circular
section, will be required, just after the gearbox, and another in
front of the engine, but this will be so no matter what the
construction may be — its function only varying. In the case
cited, it will serve to carry the underframe as well as to stiffen
and tie the frame itself, and hence must be of ample dimensions,
but if the engine is fitted directly upon the side frames, they will
only be required to act as a stiffener.

FRAMES, AXLES AND SPRINGS 331

The intermediate construction in which the unit system is
adopted will be obvious. The girders placed after the gearbox
will, in general, have to be either arched, depressed or given such
a depth that it is permissible to cut a hole in the flange of
sufficient size to. allow the propeller shaft, etc., to pass through.

It is usual to narrow the frames towards the front of the car in
order to permit of sufficient steering lock on the front wheels.

The result of this is, however, to subject the frame to a twisting
moment just at the part where the narrowing takes place, so that
some provision is here necessary. This may take the form of an
arched cross girder, or the side frames may have their upper and
lower flanges widened considerably at this point, but in many
instances both systems are adopted, although some difficulty is
often experienced in fitting the former without curtailing the
facility with which the engine can be removed, because it comes
either just in front of, or above the fly-wheel.

Some account must also be taken of the torque on the frame,
from the engine, and from the gearbox. Where these are
supported on cross members by an under frame or as in the
unit system, the design of the cross girders must involve a
consideration of the forces introduced thereby. If the engine or
the gearbox is attached directly to the side frames the forces at
the crankcase arms can be generally neglected, since they are of
small magnitude and are applied in, at, or near a point of
support. But this is not so at the gearbox, because the load and
the point of application are such that the bending moment in the
side frames produced thereby are not inconsiderable in some
cars when on low gear.

The effect upon the frame as a whole is to depress the near
side and raise the off side of the chassis, and is resisted by the
use of transverse members of ample depth, diagonal bracing,
webbing or tubular cross girders.

It will be necessary to provide a cross member in the vicinity
of the radiator to prevent distortion from being communicated
thereto, and to tie the side frames together.

195. Since the process of pressing reduces the thickness of the
metal at corners, and as abrupt changes of form tend to weaken
the material, all these should be made of ample radii — about
three times the thickness of the original plate being usually
sufficient. All rivets and bolts employed for the attachment of

832

MOTOR CAR ENGINEERING

any part or in the construction of the frame, if subject to shear,
should be made of considerably greater diameter than strength
alone would require, so as to avoid the slotting of the holes
through which they pass due to excessive bearing pressure ; and
this may be advantageously arranged for oven when in tension,
so that the load may be distributed well over the plate. Though
often neglected, it is well to use a supporting or backing plate
wherever any part is secured to the side members (see Fig. 58),
so that local distortion owing to frame movements which would
probably cause the fatigue of the metal may, to a large extent, be
eliminated.

Since the lower flange of the side frames is in tension for the
greater part of its length (and frequently for the entire length),

no holes should be drilled
through it, as its strength is
thereby decreased. It will be
generally found to be impos-
sible to avoid drilling this
flange, and therefore the width
should be increased by an
amount not less than the
diameter of the hole made.
Preferably, all * attachments
should be through the upper flange, which being in compression,
and seeing that the rivets should fill the holes, will not impair its
capacity of resisting stresses of this character. But in most
cases it is necessary to connect up to the web in order to obtain
a rigid connection, in which event the holes should be placed
as near to the centre of the web as practicable, unless the
section is at, or near a point of support, so as to remove the
metal from a part where it is least subject to bending stress,
and care is then necessary to ensure ample strength to resist
any shearing forces at this section.

196. Wheel Base and Track. — The minimum wheel base is to a
large extent limited by considerations of convenience of access
and comfort for the passengers carried and the seating accommo-
dation to be provided ; and the maximum length, by the facility
with which the car can be handled in traffic and the necessity of
having a sufliciently small turning circle.

The width of the seats from front to back requires to be at

Fig. 58.

FRAMES, AXLES AND SPRINGS 383

least 18 in. and upholstering will increase this to approxi-
mately 24 in., while comfortable leg room and side doors of
sufficient width will probably necessitate at least an additional
21 in. for the rear seats; while a similar dimension will be
none too large for the driver to ensure the convenience of access
to brake and gearbox levers, and the freedom of movement
required for the pedal gear and the steering column. Hence, in
a four-seater car the distance from the dashboard to the back of
the rear seat will be at least (say) 84 in. But the position
of the body and the engine relative to the axles merits some
attention. For comfortable riding the back of the rear seats
should be in front of the rear axle, and in order that the load on
the driving wheels may be a sufficient proportion of the total
weight of the vehicle, the engine should not project beyond the
front axle. In addition, both of these contribute to the produc-
tion of a car with a good appearance. Therefore, assuming
that the space required for the engine has a length of 24 in.,
the minimum overall length is 108 in. and any reduction
below this, excepting that brought about by the reduction in the
overall length of engine, must to some extent curtail the
measurements given above for the leg room and seating accommo-
dation, or cause the rear seats to project over the back axle —
the latter being limited by the necessity of placing the side
doors sufficiently in front of the mudguards that they give ample
space for the ingress or egress of passengers. It will be obvious
that the length assumed as sufficient for the engine will be
subject to variation with the number and diameter of the
cylinders.

Short wheel bases allow of the use of lighter scantlings,
are easily handled in service and are less expensive, but from
the necessarily small space available the machinery is more or
less huddled together, and therefore means of access are not so
convenient.

The great drawback attaching to such cars is, however, that
they have not such an easy motion as those having long wheel
bases, as the displacements of the body resulting from
inequalities of the road surface produce more marked eflFects
upon the passengers, for although the height through which the
axle may move is the same in both forms, the angular dis-
placement is less with the longer wheel base. On the other hand.

334 MOTOR CAR ENGINEERING

long wheel bases give plenty of room for access to any part of
the driving gear, and for the accommodation of passengers, but
require a larger lurning circle unless excessive angles of lock are
used for the steering wheels, and this is undesirable.

197. With regard to the wheel track employed, in exactly
the same way as, and for the same reason that increase in wheel
base produces easier motion, so also does increase in the track
of the wheels; while, in addition, the lateral stability of the
car is augmented and there is therefore less probability of a car
overturning from any cause. This latter is important, for one
may recover from a tendency to side-slip, but there is no
possibility of preventing overturning when once the motion
has begun. The wheel track must also be sufficient to allow
the necessary angle of steering lock to be obtained, and as the
minimum width between the frames is determined by the
engine and its auxiliaries, it is clear that the wheel gauge,
steering lock and maximum diameter of wheels must be examined
conjointly.

But there still remains a most important factor to be con-
sidered in fixing the wheel-track, namely, the maximum width*
of the body in the wake of the rear wheels. A low centre of
gravity is desirable, because it conduces to the stability of the car
as a whole and gives smooth running, and because the exces-
sive lateral displacement of the centre of gravity due to the
wheels passing over stretches of road having a varying trans-
verse inclination subjects the tyres to hard usage in a direction
in which loading is very destructive ; and disturbs the free action
of the springs.

To enable a low seated body and a narrow track to be
used it is necessary that the overall width should be less than
the distance between the inside edges of the tyres, as although
the turnunder of the body beneath the seats and the shape of
the tyre may apparently allow of a reduction in the wheel
track, on account of the vertical movement of the body and
clearances for mudguards, etc., very little more than this will
be practicable.

The seating width per person varies considerably in practice,
but in no case should there be less than (say) 16 in. per
person. The whole question^ together with that of wheel-
base, is, however, one that should be decided after consul ta-

FRAMES, AXLES AND SPRINGS 886

tion with the body-builder ; bearing in mind the probable
seating capacity that will be required, the types of body that
may be fitted and the advantages and disadvantages of long
and short wheelbases ; as there are so many factors to be con-
sidered that each case must be determined upon its merits. The
width of the frame will then be determined by the space
required for the springs and for the braking gear. In most
cases the frame is raised over or dropped in front of the rear
axle. The object in view being the reduction of the height of
the body above the ground. (See Figs. 180 and 184, Vol. I., and
Fig. 1 of this book.)

198. Classification of Load. — One of the greatest troubles to
the designer is that of the variation in the load that will
ultimately be carried by the chassis.

The constant load is that of the driver, the frame itself, the
engine radiator and bonnet, such portion of the steering gear
as is carried on the frame gearbox and change speed levers,
brake levers, petrol and oil tanks, fuel, water and oil and the
various fittings required for these. It will seen that the greater
part, of this load is borne by the front axles, and hence will be
of little service in propelling the car. There are also the forces
acting upon the frame by reason of the various factors
referred to in Art. 175 and which, although varying indepen-
dently, yet have a maximum value that may be considered as
constant.

The variable load is that due to the number of passengers and
the luggage carried, and will in some measure be dependent upon
the seating capacity provided. For ordinary purposes the
average weight per passenger may be taken at 150 lbs. (68 kilos),
but the luggage carried will depend upon circumstances being
governed by the conditions under which the car is employed.
Spare wheels or tyre accessories, spare parts and tools also
come under the heading of a variable load since the actual
weight carried upon the car is not constant. The greater pro-
portion of this will be carried by the rear axles.

There still remains the weight of the body, the hood, lighting
equipment, etc., to be considered. The body weight will depend
upon the seating accommodation, the type and style of body,
the material used and the fittings provided. The dimensions
allowed per passenger will also influence the magnitude of the

886 MOTOR CAR ENGINEERING

actuBl weight of the hody greatly. The variation that there
may be in the other factors mentioned will he obvious, and
require no further comment.

It will be clear that the chassis must be strong enough to
carry aafely the maximum load it will probably be required to
support, and hence entails that a certain amount of additional
weight must be carried under some cireumstanceH beyond that
absolutely necessary. This is unfortunate but is unavoidable

because chassis cannot at present be turned out to exactly
suit every condition of loading in service. In all designs an
endeavour should be made to so diapoae the load that the rear
wheels will take the greater portion. This will be a somewhat
difficult matter with two-seater cars, but by so doing much
rasping of the tyres and tendency to side-slip can be pwvented.

199. KateriaU Employed.— Frames are generally made of
either mild steel, or of nickel chrome steel. Of these materials,
the first mentioned was at One time mostly used, hot improve-
ments in the methods of manufacture have reduced both the
quality and cost of the latter as well as cost of pressing, so that

FRAMES, AXLES AND SPRINGS 337

many firms are now employing nickel chrome steel frames.
Their advantage lies in their superior physical properties and
ability to resist varying loads, albeit great care is necessary in
handling the material, since with these steels a small variation
in the heat treatment produces marked efiTects upon the finished
article. Even now the cost is high because of the higher
price of alloy steels and the more severe, gradual and repeated
character of the pressings which are necessary owing to the
nature of the material, while the elaborate annealing processes
to which it is subjected during manufacture will obviously
contribute to high initial cost.

The &ctor of safety employed for mild steel frames is from
9 to 10 and for nickel chrome steel frames from 15 to 16,
these higher values being employed partly to obtain increased
rigidity, partly on account of the indefinite knowledge as to the
exact effect of the straining actions on the frame and partly to
allow for defects that may be present in the material owing
to the distortion produced during pressing.

200. Frame Design. — In designing the side frames it is first

necessary to determine the magnitude of the loads the frame

will be called upon to support, and where those loads will be

applied, while the probable finished weight of the frame will be

^ rru ' , 11 u HP X 83,000 X 12 . ,
assumed. The engme torque will be ^^ inch

lbs. but will generally be small enough (excepting in high-
powered cars) to be neglected. The braking torque and the
limit of engine torque at the gearbox on low gear will be —

Weight on rear wheels xijlx radius of tyre divided by the
bevel gear rates, and one half is taken on each side member,
the engine torque depressing the offside and raising the near side
of the frame. These are generally applied at or near the same
point.

The maximum torque taken by the torque rod is —
Weight on rear wheels Xfix radius of tyre, and hence the
force acting at end of torque rod is —

Weight on rear wheels xfMx radius of tyre

length of torque rod '

and this force will be halved to obtain the load on each side

frame. Strictly speaking, this is not correct when the forward

point of support does not coincide with the longitudinal centre

M.C.K, 55

338 MOTOK CAB ENGINEERING

line of the chassis ; but so long as it is not far distant the error
involved is sufficiently small to be of little practical importance.

Since both side members are made of the same section for
convenience, that carrying the greatest load is considered in the
design, and this will be the offside member. On a horizontal
line mark the points of application of the loads and the points of
attachment of the springs, and find the bending, moments and
shearing forces at the sections where the loads are applied, and
plot them on a sheet of paper. Divide the bending moments at
the various sections by the permissible stress and obtain the
values of the moduli of those sections. Then equate the values
to the moduli of the sections selected (the bending moment curve
to a suitable scale will represent moduli) and determine the
necessary dimensions for the depth, using a uniform breadth of
section and thickness of plate. Make an elevation of the frame
conforming to these dimensions, taking suitable dimensions at
the ends for the attachment of the cross girders, etc., and draw
straight lines through the peaks of the curve, so that the change
of form is gradual, in order to simplify manufacture.

Lastly, ascertain that the shearing stress at any section is
below that allowable, and in so doing the web of the section
should alone be considered, since the flanges are unable to resist
this form of stress because of their slender proportions.

The method of working will be readily seen in the following
example.

201. Example.— Fig. 60 shows the loads carried by the offside
member of a chassis frame. The engine and gearbox are sup-
ported on an underframe, the forward end of which is carried at
the centre of the front cross girder and the rear end by a cross-
girder placed just behind the gearbox, so that the weight supported
on the former is 320 lbs. and on the latter 250 lbs. The weight
of driver and one passenger is taken to be 160 lbs. on each
frame and that of three passengers in rear seats 240 lbs. on each
frame.

Body weight is taken to be 1,200 lbs. distributed, over a length
of 68 in. = 17*65 lbs. per inch, the weight of the frame as
156 lbs. or 0*5 lb. per inch per member. The weight of a car
fully loaded is assumed to be 3,800 lbs. of which 2,200 lbs. is
taken on rear axle, the bevel gear ratio being 3*5 to 1, the length
pf tliQ tor(jue rod is 48 in. apd diameter of tyre is 820 mm.

FRAMES, AXLES AND SPRINGS

839

iZO Whecfbsse

'/ 03* ijl^JllL or'' f

' • — 23 >¥$ - jjrf^ *-p — 25 — I •

Fig. 60.— Diagrams of Bending Moment and Shearing Force on Fntme.

z 2

340 MOTOR CAR ENGINEERING

Force acting on end of torque rod is
2.200 X 0-45 X 410 _ ggg ^^^ / 340 i^g )^ or 170 lbs. on

25-4 X 48
each frame.

Limit of engine torque is

2.200 X 0-45 X 410 ,^g j^^j^^^ ^ 4 gg^ ^^ ^^^,,,38,
25-4 X 8-5
If tlie width of frame is 8 feet, the force on each side

member is

— '-- p; = 127 Ibf.
2 X 18

The reactions at the spring attachments will be equal at each
end of each spring, and thus magnitude may be attained by taking
moments about (say) the front of the chassis, calling reactions
at front springs Ri and at the rear springs Rj.
R, X 82 + Ra X 117 + Ra X 155 = (85 X 18) +(160 X 16) +

(50 X 50) + (20 X 75)
+ (127 X 78) + (125- X 78) + (160 X 82) + (170 X 88)
+ (240 X 182) + (50 X 149) + (600 X 111)
4. (77-5 X 77-5)
82R- + 272R2 = 166,487-25. „ „ x

Total loud on the offside member = 1 ,814-5 lbs. = 2 (Ri + Ra)-
Hence Ri + R» = 907-25

and Ri = 907-23 - «*•

Bv stibstitution —

82 (907-25 - Ra) + 272R2 = 166,487-25

Ra = 572 lbs.

and Ri = 8^^ '*'«•

Hence, the reactions at a and d (Fig. 60) are each 335 lbs.,

and at «i and r are each 572 lbs.

202. The bending moments at any section of the frame are the
algebraic sum of the moments of the forces acting on either side
of that section (see Art. 19). Moments having such a direction
relative to the section under consideration, that their motion is
clockwise, will be termed +, mid those in a reverse direction -.
If negative they will be plotted on diagram Iwlow the line, and if
positive above the line.

Then B.M. at a = 0,

B.M. at t = (- 335 X 13) + (13 X 05 X 6-5) = -

4,313 inch lbs.

FRAMES, AXLES AND SPRINGS 341

For the first term, since the reaction at a is anti- clockwise,
therefore negative, and acts at a distance of 18 in. from h.
As regards the second term, (13 X 0'5) is the weight of that
portion of the frame between a and h, and its moment about h is
the same as that of an equal mass concentrated at ihe centre of
gravity of that portion of the frame, that is, at midway along its
length — 6*5 in. from h.
B.M. at c = (- 335 X 16) + (35 X 8) + (16 X 0*5 X 8) =

— 5,131 inch lbs.
B.M. at d = (- 335 X 32) + (35 X 19) + (160 X 16) + (32 X

0-5 X 16) = — 7,239 inch lbs.
B.M. at c = (- 335 X 50) + (- 335 X 18) + (35 X 37) + (160

X 34) + (50 X 0-5 X 25) = - 15,420 inch lbs.
B.M. at m = (- 335 X 117) + (- 385 X 85) + (35 X 104) +
(160 X 101) + (50 X 67) + (20 X 42) + (252 X 39) + (160
X 35) + (170 X 29) + (117 X 0*5 X 58*5) + (40 X 8*82 X
20) = - 12,904 inch lbs.

The procedure employed will be clearly seen from the above.
Negative moments in this case will mean that the upper side of
the frame is in compression and the lower side in tension. If the
forces acting on the left hand side of the sections had been con-
sidered, positive moments would have been obtained on the
assumption that clockwise moments are positive.

Plotting these quantities on a straight line base, the curve
seen below in the figure is obtained. Supposing that the frame
is pressed from 72 ton steel, and a factor of safety of 10 is allowed,
the stress will be 10,000 lbs. per square inch ; and since B.M. =
/Z, the curve will represent the moduli of the sections if the scale
is divided by 10,000.

Next select a section for the frame of suitable thickness and
width, say channel section of 0*15 in. in thickness and 1'5 in. width.

Then „ JBH^ - hh^

Z= ^

B = 1-5 in., fc = 1-5 — 0-15 = 1-35 and L = H - 0-3 in.

„ „ 1 1-5 H^ — 1-35 (H - 0-3)8

Hence Z = ^ • ^—

o 11

= 0-025 H» + 0-2025 H^ — 0'06075 H -f 0'006075

0-006075

= 0025 H^ + 0-2025 H - 006075 +

842 MOTOR CAR ENGINEERING

The value of the last term can generally be neglected on
account of its small value with the thin sections of metal
ordinarily used.

Then equating Z to the values of the moduli obtained from the
curve in diagram.

For section at b :— 0-025H2 + 0-2025H - 006075 = 0-4318 ;
at c, Z = 0-5191 ; at r7, Z = 0-7239; at <?, Z = 1-542 ; and at wi,
Z = 1-2904. By plotting values of H, it may be ascertained
that the depths of frame at fc, c, rf, e and m are 1*51, 1*8, 2*5,
4*8 and 4-06 respectively. Determine the depths of frame at the
other points of application of load and insert these as shown in
diagram, setting out a suitable dimension at some point between
a and h for the attachment of the dumb iron, at r for the attach-
ment of cross girder and shackle for spring, the heavy line will
then represent the shape of the finished frame if a straight upper
surface is used. As a rule, however, the front end between a and
b is curved downwards, and a set is often put in at or near the
rear axle. Care should be taken that the width of the frame is in
no place less than that calculated.

208. For the shearing force diagram, it has been stated in
Art. 19 that the algebraic sum of all the external forces on one
side of any section is the shearing force at that section.

At a the shearing force is 835 lbs. ; at & it is 385 lbs. minus the
downward acting force (18 X 0-5) = 828 lbs. ; at c it is (885 — 35
— 8) = 292 lbs. ; at d it is (385 — 35 — 160 — 16) = 124 lbs. : at e
it is (385 + 835 — 85 — 160 - 25) = 450 lbs. ; and at m it is
(885 + 885 — 85 - 160 — 50 — 20 - 252 — 160 — 170 - 58*5 —
352-8) = - 588-8 lbs.

These values should be obtained at every section where a load
is applied, the results plotted as shown on diagram, and the
section checked for strength wherever any holes are drilled
through the web, as for the attachment of cross girders, brackets
or springs for the passage of rods.

If it is necessary to pierce the lower flange (that in compres-
sion) the section at that part must be examined, and where
necessary the webs should be increased by at least the diameter
of the hole employed. Very frequently it will be found that
little, if any, addition is required to resist bending and shearing
stresses.

204. Cross Girders, etc. — Having determined the general dimen-

FRAMES, AXLES AND SPRINGS 343

sions of the side members, it is necessary to arrange for the
cross girders, webs, fillets, etc., for the purpose of stiffening Jip
the frame and preventing distortion and to allow for the indeter-
minate forces acting upon it, which were referred to in Art. 193.
These must depend for their position and construction upon the
judgment of the designer, and as regards their strength in many
cases experience dictates what dimensions should be employed.
But where a definite load is supported, as, for example, where the
front cross girder in example shown supports the front end of the
underframe and the cross girder behind the gearbox supports the
rear end of underframe, the part should be designed to carry the
load. The front member is a beam free at the ends and loaded
in the middle, while the rear member is a beam free at the end
carrying a load at two points by the weight supported on the
underframe and at another point by the force transmitted to the
end of the torque rod by braking. There is also a force applied
at the point of support of the brake, but its effect is indefinite,
and probably only tends to slide the gearbox or other part to
which it is secured in a transverse direction. In any case it is of
little moment, and is allowed for in the low stress always used.
Hence, by taking moments about the two ends and finding the
reactions at the points of support of these girders for the loads
mentioned, the stress at any section of them may be determined
in a manner similar to that already described for the longitudinal
members.

205. Springs. — The functions performed by the springs upon
which the frame is carried have been referred to in Art. 247, and
the use of shock absorbers has been explained in Art. 248, Vol. I.,
to which the reader should refer. It will be seen that the springs
serve to absorb the irregularities in the contour of the road sur-
face, absorbing the shock and giving an easy motion to the body
as the car progresses. For this purpose plate springs are
eminently suitable, as they have great capacity of storing up and
restoring energy, while the friction between the leaves allows the
motion to be transmitted gradually to the body, which would not
be the case were helical springs alone employed.

The suitability or otherwise of a spring largely depends upon
its period of vibration, and lengthening the springs or increasing
the deflection under any given load increases this, but at the
expense of a greater tendency to roll, and thus introduces effects

344 MOTOR CAR ENGINEERING

that are undesirable. Further, a spring suitable for use on
smboth roads would be less suitable for employment over rough
surfaces or in a district where granite setts predominate, and as
cars are not usually confined to one class of road it is obvious
that they must be designed to give efficient service under
varying conditions of road surfaces. This is a difficult matter,
especially as the weight of the supported mass varies con-
siderably in practice, while the variation in the speed of
the car only serves to complicate the matter still further.
The design must therefore necessarily be based largely on
experience.

The object of fitting shock absorbers is to increase the period
of the springs by introducing an additional frictional medium to
retard the rise and fall of the axle, and they are especially suitable
where the road surface is undulating. Supplementary springs
are fitted in order to absorb the smaller inequalities of the road
and operate by reason of the fact that there is no frictional
damping action between the coils of wire composing the spring.
They thus give life to the springs, taking up the road shocks that
would be transmitted directly to the body and leaving the main
springs, which may then be made harder, to perform their
ordinary function unimpaired.

206. Helical Springs. — As the result of investigations made by
Mr. Wilson Hartnell with helical springs for governors, it has
been found that 60,000 to 70,000 lbs. per square inch (42-2 to
49*2 kilos per mm.^) is the safe stress for springs of f in.
wire, and 50,000 lbs. per square inch (35'15 kilos per mm.*) for
i in. wire, while the moduli of rigidity vary from 11,000,000
for I in. wire to 13,000,000 for Jin. wire.

In helical springs the wire is subject to torsion and in spiral
and plate springs to bending.

If ii is the diameter or 8 the length of the side of the wire, D the

mean diameter of helix, W the load in pounds and n the number

of free coils,

WD
The twisting moment on the wire is -^.

The resistance to torsion is y,, f/P for circular wire, and
0*208 f^s^ for square wire.

FRAMES, AXLES AND SPRINGS 845

WD ir ,M J WD „ „nQ ^ 8
"2 ~ re-^' "2- =0-208 /y

; _ AyiUVD _ //■

^ ^ 2ir/; « - -V 0.208/^ 2

^ 0S9f. ^ 0-41 GX

from which, on knowing the stross to be emploj-ed, the necessary
diameter may be obtained.

If $ is the angle of torsion through which any one coil is twisted,
8 is the deflection per coil and I is the length of wire in one
coil —

2/7
But $ = ^, I = ttD nearly, and the twisting moment

lJ.'l^.

2 16

,, ^ ,. WD X 16
so thatX = -2^^—

Substituting this value of/, and the value of in

Q\VJ)3

we have S = -^-rrr for round wire.
For square wire — S = -- ^ as before.

^ = l^^ = 0-208/.».
whence, as before, it may be shown that

The total deflection will be the deflection per coil multiplied by
the number of free coils.

It will be observed that round steel is more economical of
material than square steel.

207. Plate or Laminated Springes. — This class of spring is used
in several forms, of which the principal are — the semi-elliptic, the
full elliptic, the three-quarter elliptic and the cantilever spring.
The first- mentioned has, perhaps, the most extefisive employment,

346 MOTOR CAR ENGINEERING

and is found iq three forms. I,n the first the two ends are attached
to the frame, in the second the two ends rest on the rear axle
casing and the centre supports the centre of the rear cross
member, and in the last the front end only is secured to the
frame and the rear end to a cross spring attached to some point
on the centre line of the chassis — this latter arrangement being
only employed for the rear springe.

In some designs, where the three-quarter elliptic is used, the
upper qunrter takes the place of a dumb iron, being directly con-
nected to the frame. The object of employing these variations of

Fio. 61.— 12-16 h.-p. Armstrong- Whitworth Front Axle and Steering Q«ar.

the commoner semi-elliptic spring is to obtain increased easiness of
suspension ; at the same time the tendency to roll at the corners
is rather more pronounced, excepting in the cantilever or inverted
semi- elliptic, although this depends largely upon the design.
The advantage of the cantilever or Lanchester spring lies in the
fact that the deflection of the spring, due to axle movement,
only transmits about one-half of that displacement to the frame.
The front end of a semi-elliptic front spring is pivoted directly
on the frame, and is rendered necessary because of the drag of the-
wheels, while the rear end of these springs will be shackled. A
similar construction is often found at the rear springs,
but is not imperative, and in some designs both ends are

FRAMES, AXLES AND SPEINGS

848 MOTOR CAR ENGINEEHING

shackled. With the full elliptic springs the centre of the upper
half is secured to the frame, and to resist the tendency to lateral
movement a parallel motion is sometimes fitted (see Fig. 189,
Vol. I.) between the side frames and the differential casing, while
in the Austin the front end of the spring is hinged on the frame.
For cross springs, the rear end of the side spring will require to
be fitted with a shackle allowing movement in two directions at
right angles, and this should be arranged so as to be in tension.
It is preferable that all shackles and links be in tension, though
often this is rather a difficult matter, but is overcome sometimes
by curling the end of the upper spring over in the form of a scroll.
It is advisable to fit a piece of softer metal or fibre on the seats of
the springs. Methods of assembling the springs in positioTi are
to be seen in Figs. 57, 59, 61 and 62, and in Vol. I.

As a general rule springs are bedded down upon pads formed
on the upper side of the axle or axle casing (see illustrations),
but in several instances the underslung type is employed.

Ample-sized lubricating devices should always be provided and
of such a form that the lubricant is introduced to the centre of
the pins, which should themselves have large bearing areas.
These pins should be provided with some device to prevent turn-
ing, such as by forming a pear heck under the head or fitting a
pin stop in that position.

If the latter is used it is preferable to introduce it by drilling
through the head so that one half is recessed into the pin. Some
means are also necessary to prevent endwise movement or the
slewing of the laminations.

End movement may be prevented by a pin passed through the
centre of the spring (see Fig. 59) or by a pin well up on the
leaves. The latter will suffice for both end and side displacement,
but the former will need to be supplemented by clips on the
springs.

208. Design of Laminated Springs. — The maximum stress
allowed in springs subject to bending is often up to practically the
elastic limit of the material, as much as 80,(X)0 lbs. per square
inch (56*2 kilos per mm.^) being safely carried under maximum
.load with carbon steel. Springs are often so designed that when
the elastic limit of the material is reached the laminations are
straight.

The factors to be considered in the design of a spring are — its

FRAMES, AXLES AND SPRINGS 849

strength to support the load, its period to give an easy motion to
the car and its resilience in order that it may be capable of
absorbing sufiBcient energy in operation.

For /Str«72/7f/i a semi-elliptic spring is a beam supportedat the ends

and loaded in the centre — therefore the bending moment at the

WL
point of application of the load will be —r- , where W is the total

supported load and L is the distance between the points of support
— in this case the pivots or shackles.

The resistance offered to bending by a rectangular section is

^ W<y, where b is the breadth and h the depth of ihe section, and as

th3re are several such sections in a laminated spring, the total

resistance = j, hh% where n is the number of plates.

.-. WL' = H hh'f
4 rt '

and hlr = -^— ^ ,

in which all the terms on the right hand side will be either known

or may be assumed, and hence the value of hh^ can be

determined.

Butitis desirable that a uniform intensity of stress be maintained

at every cross-section through the spring. In manufacture these

plates are all bent to the same radius of curvature, that is to say,

they all have the same curvature on one side of the spring.

This will cause the outer or under side to be a flatter curve than

the inside, so that when assembled a space will exist between

them at the centre until pulled together by the spring clips.

/' E
They then still have the same radius of curvature, and since = t)

1
the stress is proportional to p , and the induced stress in all the

laminations is constant.

To maintain this uniformity of stress under load it is necessary
for the modulus of the section of Ihe spring at any point to be
proportional to the bending moment, and this is proportional to
the distance of the section from the points of support. The
modulus of tUe section is, however, proportional to th^ number of

860 MOTOR CAR ENGINEERING

laminations in the spring at that section, and hence the number
of laminations present must decrease as the distance from the
centre increases. This is arranged for by shortening each
successive lamination by an amount equal to the distance between
the ends of the longest leaf divided by the number of laminations.
This does not, however, give a suflBciently close gradation of the
modulus of the section, so the ends of each lamination are
tapered off.

For Period. — This, as has been previously stated, depends
upon the kind of road over which the car is employed, the speed,
the class of vehicle, etc. The time for a complete oscillation may
be determined from the formula

t = 27r V -

where t is in seconds and I is the deflection of the spring
between no load and full load in feet. Mr. Lanchester ^ states
that he has " found in practice that a period slower than 90 per
minute gives an ample degree of comfort, whereas a period
quicker than 100, although frequently employed, should be
avoided where circumstances permit." These periods corre-
spond to deflections of 4"85 ins. (110 mm.) and 3*52 ins.
(98 mm.) respectively.

The deflection of a semi-elliptic spring may be determined by
considering only the longest leaf and treating it as subject to the
total load divided by the number of laminations. The central

deflection of a beam is 5-^ . M = — - and I = zr^ hh\

8 EI n 4 12

Hence = ^ -uTfa
8 nEbh^

A JIB 3 WL3

and hh^ = -- 5^.

From above bh^ = ^ - . .

2;?/

Therefore, by division h = jr;' ,

from which h may be evaluated when /is known and by substitu-
tion the value of h may be ascertained.

For Resilience. — The energy stored up in the spring' when in

1 fcfee Proceedings I,A,L\, Vol. II., p. 193.

FRAMES, AXLES AND SPRINGS 851

its position, of rest is the product of one-half of the supported mass
and the deflection, and this is equal to

6 E ^ ^^'""^^ = 6E ^ -2-

For successful operation the energy per cubic inch of the
material when the spring is in this condition should not exceed
5 feet lbs. and preferably less.

1 f^
Hence ^^ = 5.

If E = 80,000,000

/= \/80E

= 30,000 lbs. per square inch.

If only 4 feet lbs. per cubic inch of metal is stored up in this
stationary position, the stress should not exceed 26,800 lbs. per
square inch for the above value of E. This does not indicate the
maximum stress, for when the spring is deflected in action the
stress will rise considerably higher.

209. Fixed Axles. — These may have either an H or a circular
section, and in the latter form may either be solid or hollow. If
the solid circular form is employed, a tie rod is usually placed
beneath the axle (see Fig. 157, Vol. I.), to render it suflBciently
strong without excessive weight in this part, which is a dead-
weight on the tyres.

The load upon the axle is principally vertical, as although
heavy blows may be experienced by the tyres, the forces
acting in a horizontal direction can hardly normally exceed the
product of the supported weight and the coefficient of friction
between tyre and rOad ; but these will depend upon the magnitude
of the obstacles encountered and are largely indeterminate. .For
vertical loads, the H section is superior to the circular form,
which is however equally strong in all directions ; but on account
of its greater mass, or the difficulty in attaching parts to it
without adding greatly to the weight, or the possibility of
defective attachment with solid or tubular axles, the H section is
more in evidence. It is generally constructed as shown in
Figs. 61 or 62, in which it will be noted that the forked end is
formed upon the stub axle, the end of the front axle being simply
a boss through which the steering pivot pin passes. This gives a
cheaper metho4 of manufacture than when the fork is formed on

352 MOTOR CAK ENGINEERING

the axle, since it is easier to handle the smaller stub than the larger
main axle. Pads are provided for the attachment of the springs,
and the axle is cranked as may be required to secure a low
suspension for the engine and framing, while allowing the
necessary clearances for the full vertical movement of the frame,
etc., without causing contact with the axle.

The front axle is designed for bending stresses. Let Wi and
W2 be the loads supported and Li, L2, be the distances between
the springs and the centre line of the wheels.

The reactions at the wheels are

^ _ W2^(L2_-:J.i) . Wi (L2 + Li)
"^^ "" 2L2 ' "^ 2L2

^ _ Wi (L2 - Li) , W2 (L2 + Li)
^^- 2L7 "^ 2L2 ~ "•

Then the bending moment at any section may be found by
considering the forces acting on one side of that section
exactly as was shown in Art. 202 for the side frames. It will
be found that the bending moment curve will be a straight line
between the springs. Usually, the load carried by the offside
spring is not greatly in excess of that on the near side spring, and
since the springs are symmetrically arranged on the axle which
is made of uniform section throughout to take the greatest bend-
ing moment, it is sufficient to consider them both as equal in
magnitude to the greater. Un«ler these conditions the reactions
will be both equal to Wi, and the bending moment at any section
between the points of loading will be constant and represented
on the diagram by a horizontal straight line of magnitude

Then, equating the bending moment to the moment of
resistance of the section, the dimensions necessary to withstand
the load can be ascertained. The stress should allow a factor
of safety of 8 to be employed, and preferably 12 in higher grades
of alloy steel. To obtain the necessary rigidity in a horizontal
plane the overall depth of the section in H girders should be not
more than 1*5 times the greater breadth, preferably the breadth
and depth should be equal. The thickness of the web of the axle
should be not less than one-fifth of the breadth.

210. Stul) or Swivel Axles.— These fti^ providec( in order to

FEAMES, AXLES AND SPRINGS 358

allow of the steering of the car being efficiently performed. Two
arrangements with different methods of mounting are seen in
Figs. 61 and 62, and others are shown in Vol. I. The attach-
ment to the axle may be either by a forked connection as referred
to in the previous article, or by the use of a conical or parallel
vertical pin formed on the swivel axle, which works within a
coned or parallel hole in the end of the main axle. The latter
form is not, however, very often employed. The wheel may run
on plain bearings or upon ball-bearings — the latter method being
general in pleasure cars; and not infrequently, a double row
ball-bearing is placed close up to the junction with the fork
because this bearing takes the greater load. The two ball-bear-
ings should be placed as far apart as possible, and rigidly retained
at their correct distance by a sleeve piece, as shown in the illus-
trations. If plain bearings are used, it may be assumed that the
load is uniformly distributed and sufficient area provided so that
the intensity of pressure does not exceed 200 lbs. per square inch
(•14 kilo per mm.*) in order to keep the side thrust from affect-
ing the motion of the bearing too much adversely. Boiler-
bearings are for this purpose excellent, while ordinary ball
thrusts are cumbersome.

The load on the axle is usually taken upon a ball-bearing which
may be placed either within the fork or above it. The swivel
pins should be hardened, as should also be the bushes in which
they work, and both must be pinned to prevent rotation. Ample
lubrication should be employed, and the arrangement must be
such that it can be assured that the lubricant is being carried to
the part. Devices should be provided wherever possible for
excluding dust and grit which greatly diminishes the length of
efficient service of the joints.

In order to reduce the load on the steering gear, and hence the
effort required to move the wheels, the plane of the wheel and
centre line of the pivot are not usually parallel, but inclined so
that the centre line of the pivot meets the ground in the plane
of the tyre. This may be achieved by either sloping the wheel
or the pivot independently or in combination. In one other form
the pivot is placed within the hub of the wheel, but this, while
giving perfect steering, is attended by the disadvantage of the
increased size of hub required.

The centre line of the steering pivot should strike the ground

M«G.Ei. A A

354 MOTOR CAR ENGINEERING

in the plane of the wheel, as previously observed and should
intersect the plane at a point just in front of the centre
of area of contact of tyre and road. This necessitates that the
pivot should be inclined at an angle of 2 or 3 degrees with the
vertical and is necessary in order that the wheels may "track"
correctly even though there be a large amount of play at the
joints, or if by any chance the tie rod should be disconnected in
running.

The maximum loads under ordinary conditions of service are
not excessive, and the proportions are determined rather by the
necessity for providing sufficient bearing surfaces, symmetry and
experience. The load on the wheel is proportioned between the two
ball-bearings fixed over the axle inversely as the distance between
the centre line of the wheel and the centre line of the bearings,
but as the inner ball race is usually close up to the centre line of
the wheel it carries the greater proportion of the load. If
designed for the bending moment on this basis, the axle will be
much too weak.

But there is one condition that must be provided against, that
is sidesUp when rounding a corner or on an incline. When
the tyres are about to slip upon the ground there is a force
acting at the point of contact equal to W/x. Hence the bending
moment is W/xR, where W is the supported weight, fx is the
coefficient of friction (say) 0'45, and R is the radius of the tyre,
and the section of the axle at the edge of the inner ball race
must be sufficiently strong to withstand it.

Therefore, W/xR = ^ W

where D is the diameter of the axle at the section considered,

and /is the stress which should allow of a factor of safety of 8.

Care should be taken that W, R, D, and / are all in the same

uuits of measurement. The axle may then be coned as is

desired or convenient for arranging the outer bearing.

This also applies to the steering pivots which are subject to

shear. The moment W/xR is transmitted through the wheel and

WuR
the stub axle and produces a shearing force of — y" - on the pin

where L is one-half of the distance between the two sections
of the pin under shear (or the radius at which the force is
applied),

FRAMES, AXLES AND SPRINGS 855

The area of the two sections is

Therefore ^ = ^ /.

from which the value of A may be determined. // should
allow of a factor of safety of from 10 to 12.

211. Torque and Badins Rods. — The elementary function of the
torque rod is to take the reaction of the torque on the axle cas-
ing, either when running or during braking, while the radius rods
are fitted so that the driving force at the tyres will be trans-
mitted direct to the frame and to keep the rear axle in correct
alignment across the car.

The arrangements and details employed are very numerous.
In some cases separate rods are fitted to perform the separate
functions of resisting torque and transmitting the drive, in which
event the torque rods will be placed at or near the centre of the
car and the radius rods towards the side, whilst in others two
radius rods fitted at the extremities of the axle serve the double
purpose of torque and radius rods.

Occasionally the propeller shaft is enclosed by a tube or
casing, and may take the torque alone or both torque and drive.
Some designers allow the springs to take the drive, and some
permit both torque and drive to be transmitted through the
springs. These do not exhaust the many arrangements employed,
but serve to show what a multiplicity of designs are possible.
To cause in any way the load upon the springs to be augmented by
either torque or drive is, however, considered to be objectionable,
because a harder suspension must, by so doing, be obtained,
while in addition the movement of the rear axle is not correctly
governed, as will be seen later, so that the excessive work is
thrown upon the sliding joints in the propeller shaft ; albeit it
has the effect of cushioning the drive, since the flexibility of the
springs absorbs variations in the torque when running. When
the springs take the place of radius rods, or instead of both
torque and radius rods, they will require to be hinged at the
front end to allow for the deflection, shackled at the rear, while
if used for torque alone they may be shackled at both ends. In
both instances the necessity for a rigid connection between the
springs and the axle is emphasised.

Wherever a radius rod is used, the attachment to the frame

A A 2

856 MOTOE CAR ENGINEERING

must be pinned and not shackled, while torque rods should be
connected through the medium of a link, preferably allowing
movement in a longitudinal and a transverse direction. In
order that the rise and fall of the axle may be quite free and
unrestrained, and the movement of the sliding connection in the
propeller shaft as limited as possible, the front end of all torque
and radius rods or tubes should be in line with the forward
universal joint in the propeller shaft. Unfortunately, this is not
always the case, but it is desirable to obtain such an arrange-
ment. Further, it is desirable to fit buffer springs on the end of
the torque rod in order that the drive may be taken up or the
car braked gradually, and thus reduce the wear and tear upon the
tyres.

The reader may refer to two articles' on ** Torque and Radius
Rods " that appeared in the Automotor Jtmrnal for 20th and 27th
of January, 1912.

The torque rods are correctly attached to the axle casing, the

upper tie rod is in compression and the lower tie rod in tension

when braking. The limit of braking is reached when the wheels

just commence to slip upon the ground, and the braking force is

Wm— the braking torque being WfxR. If the torque rods are

tangent to a circle of r inches or mm. radius, the thrust on the

R
rod is W/x — ^2, since the rod in tension should take one-half of
r

the torque. The rod may then be designed according to Gordon's

formula. The bolts or studs attaching the rod to the axle may

be examined for shear, while the support at the forward end will

be in tension, the force applied being

WmR

2 r L

where L is the length between the centre of the axle and the

point of support.

For the radjus rods the tptal force acting at both wheels is

W/x, and one-hall of this is taken by each radius rod so that the

Wm
rod is loaded with an end thrust of -^, and may be designed

using Gordon's formula.

It should be noted that where torque rods are placed other
than on the diflferential casing, the whole of the axle casing is
subject to torque.

CHAPTER XVII

STEERING GEARS

212. Geometrical Properties of Steering Gear. — The condition
for correct steering is satisfied when all four wheels roll upon
the ground without sliding, that is, the wheels all roll about
the same centre ; and since the direction of the two rear wheels
is fixed, the centre of rotation must lie on the axis of the rear
axle produced. Therefore, the steering gear should be capable of
giving such a relative angular motion to the front wheels as will
cause the axes of the stub axles when produced to meet on the
axis of the rear axles produced. As a matter of fact, the gear
now used on automobiles is incapable of imparting these motions,
and hence some lateral sliding is bound to take place; conse-
quently, some risk of sideslipping is always present together
with wear on the tyres. The aim of the designer should there-
fore be to reduce the magnitude of the error in the steering,
although his efforts in this direction will be seriously impaired by
three important factors. Firstly, that the tyre makes contact
over a surface and not at a point, therefore, even with a perfect
gear, some slipping would be inevitable ; secondly, that the
wheels are almost universally set closer together at the front
than at the rear for the purpose of correcting the disalignment of
the wheels on account of the elastic strain in the mechanism
from the drag when travelling. From this cause they may be
non-parallel to the extent of half a degree when the car is
stationary; thirdly, the wheels themselves are often sloped so
that the intersection of the axis of the pivot strikes the ground
just in front of the centre of area of contact of the tyre with
the road.

218. Steering Lock. — The first consideration in the design of a
steering gear is the maximum steering lock to be given to the
wheels as this determines the minimum radius of the turning
circle.

358 MOTOR CAR ENGINEERING

Let p be the pitch of the steering centres, tv the wheel base, and
R the radius from the centre of rotation to the centre of the outer
steering pivot (see Fig. 68).

Then, in turning, the outer rear wheel will move about a centre
0, such that the radius of its circle will be OD plus the distance
between D and the centre of the oflf road wheel ; while the outer
front wheel will move along a circle of radius OB plus the
distance between B and the oflf front road wheel. Thus, the
minimum space required is OD + OB + 2 (distance between
B and the centre of the road wheels). The angle of lock to be
given to the outer steering wheel, or the value of OB may be
found from

OB = BD cosec 0,
i.e.y R = ?(7 cosec 0.
Also OD = w cot 0,

The angle of lock to be given to the inner wheel will depend
upon the angle of lock at which correct steering is to be pro-
duced, and this is considered later. The angle (p will always be
greater than 0.

Usually, the radius of the turning circle will be determined by
the designer, but in some classes of work the maximum turning
circle is fixed, and the necessary lock to enable the car to turn
without reversing must then be ascertained. This will be found
to limit the length of wheel base, especially as the pitch of the
steering centres cannot be reduced to less than a certain value,
depending upon the space required for the engine and the
clearances necessary for the wheels. A small turning circle
facilitates handling in traffic, but excessive angles of lock are to
be avoided because of the high loads that may be thrown on the
gear in using them. It is preferable not to exceed a maximum
of 40 degrees.

214. Setting out Steering Gear. — It has been stated in Art. 212
that the form of steering gear employed at the present day does
not give perfect action but that the errors should be reduced to a
minimum. If any system is examined it will be found that the
point of intersection of the axes is on the forward side of the rear
axle at the commencement of the movement, but as the angles of
lock increase, the point approaches the line through the axis of
the rear axle, the error increasing in so doing up to a certain
maximum and then decreasing to zero when the line through the

STEERING GEARS 359

rear axle is reached, and then rapidly recedes towards the rear
with large angles of lock. Thus, there are three positions of
correct steering — one when the wheels are directed straight
ahead and the car may be assumed to be moving along the cir-
cumference of a circle of infinite radius, and the other two when
the axes of the pivots intersect with the axis of the rear axle pro-
duced at the same point. This always occurs if the angles of
lock are carried far enough as they should be. It is therefore
necessary to first determine the maximum angles of lock desired
or required, then choose the angle at which true steering is to be
obtained, and finally to find the proportion that must be given to
the levers and tie rod, so that the total error involved is partly in
one direction at the start and partly in the oj^posite direction at the
finish. To divide the error approximately equally on the two
sides the position of correct steering should be taken at between
0*75 and 0*8 of the maximum lock, and if any other sub-division
is employed it should be noted that the errors with large angles
of lock increase much more rapidly than with the smaller angles.

215. — Let the angle of lock to be given to the outer steering
wheel for correct steering be known. Then from Fig. 63 the
relation between 6 and <^ at the positions for true steering are
found as follows : —

ED = BD cot and EC = AC cot <f>
CD = ED - EC = BD cot ^ - AC cot </»
Hence CD =.p=. w cot 6 — xv cot <f>

cot 6 = cot ^ — — .
^ w

It will be observed that this is quite independent of the lengths
of the steering arms.

The length of the tie rod FG is AB — 2AF sin a

= 2) — 2r sin a.

216.— For the angle a between the steering arms and the axis
of the vehicle it is necessary to consider the two cases —

(a) When an internal coupling rod is fitted,

(b) When an external coupling rod is fitted,

since the relative motion of the two wheels is not the same for
both positions of tie rod.

The dotted lines in the figure represent the gear when in the

f r

360

MOTOR CAR ENGINEERING

a>
o

fee

flS

9SBqi99lfM ^

STEERING GEARS

361

position of true steering. Let r be the radius of the steering
arms and join BH.

Then - BH« = EH" + EB"

= EH« + (AB - AE)>
= EH" + AB" - 2AB . AE + AE"
= ?•" sill" (90 — o - <^) + / — 2;)/- cos (90 — a—^)
+ r cos" (90 — a — <^)

= ?^ J sin^ (90 - a - <^) + cos^ (90 -a - <^)[ + ^

— 22>r cos (90 — a — <^)
= ^-^ + jy^ — 22)r sin (a + <^) . . . (i)

cos EBH =

_ 1^ + (BUf - (EH)^

2/13H
_ 2?-^ + P^ — 2rj? sin (<^ + a) — p' + 4rp sin a — 4/-^ sin^ a
"" 2r V?-^ + !>'' — 2r^ sin (<^ + a)

_ r — p sin ( <^ + a) — j?^ + 4yy sin a — 4i^ sin^ g

Vr^ + i>^ — 2?y sin (<^ + a)

r (1 — 2 sin^ a) +i> ] 2 sin a — sin (</» + a)

Vr^ + i^^ — *^''i> sin (<^ + a)
Similarly

cos HBA - i>^ + (BH)^-r^
cos UJ3A - ,^^^^ jj

p — r sin ((f) + g)

Vr^ + P^ — '^'i^ sin (<^ + g)

Supposing that we use the angle 7 as a basis of calculation,
the angle fi will be the negative error or the angle 7 the positive
error.

Error 7 = GiBG -0 = GiBA + u — {0+ 90°).

For internal coupling rods. — Galling the angle GiBH = M and
the angle GiBA = N,

Error 7 = M + N + a -(0 + 90°)

cos M =

cos N =

r (1 — 2 sin* a) -{- p -. 2 sin a — sin (<^ + a)

Vr* + p^ — 2rp sin (<^ + a)
p -— 7' sin (<^ + g)

V)^ + i?^ — 2/2? sin (<^ + a)

362 MOTOR CAR ENGINEERING

Error i8 = M + N + </» + a — 90°

cos M =

r (1 - 2sin2 a) + i> j 2 sin a - sin (a - ^) [

Vi^ + ;>* — 2rp sin (a + 0)

cos N = . ^ ^ ^ ^ -

V?-^ + p^ — 2779 sin (a — 0)

For external coupling rods.

Error 7 = 90° + « - (M + N + 0)

r (1 — 2 sin^ cl) + p \ sin <^ + a) — 2 sin a) Y

cos M = , ■- '

V/-2 + P^ + '^rp Bin (<^ + a)

XT p + r sin (<b + a)
cos N = , _ ^ ' --^-^ ' ^^ _.

V a-^ + 1> + 2^/* sin {(j) + a)
Error ^ = <^ + a + 90° - (M + N)

cos M =

r (1 — 2 sin^ «) + J^ ] sin (a — ^) — 2 sin a

Vr^ + p^ + '^rp sin (a — ^)
XT' '^ + 7> sin (a — 0)

cos N = -77 -- V— ^^ — 3r-_rr

V?^n^^ + 2rp sin (a - 0)

The above expressions appear at first sight to be unwieldly,
but they are not so in practice. It will be found after some
experience that it is quite easy to estimate very closely the
figures which will give the best results.

It is usual when setting out a steering gear to assume in the
first instance that the steering arms meet on the centre line of
the back axle and calculating for this position, then adjusting as
may be found necessary.

It may be noted that a long wheel base reduces the steering
error.

217. Steering Levers, Rods, etc. — For true steering the length
of the tie rod must be determined, so that geometrical
conditions are satisfied with the values of p, w and r selected.
The pitch of steering centres and the wheel base will be settled by
considerations other than those of steering, and the length of the
steering arms by the convenience of using such a dimension. A
limit to the value of r for external rods is imposed by the
desirability of keeping the centre line of the wheel as near to the
steering pivots as possible, as well as the necessity of employing

STEERING GEARS S63

a relatively large angle of a in order to obtain true steering.
Hence, a must be determined for an assumed value of r, the
arrangement being examined to ensure that the necessary clearance
between the extremities of the lever and the wheel are available.
Generally, it will be found that with external rods the length of the
steering arms must be less than with the internal system, bat it

Fio. 64. — .\rm8trong- Whit worth Steering Gear.

should be noted that the longer the arms the less the load on the
rod.

As regards the relative advantages of the external and the
internal system, the latter entails subjecting the rod to a compres-
sive stress in straight ahead running, but removes it to a position
in which it is guarded against damage in the event of a collision,
while the load can be reduced ; but in many cases it is neces-
sary to crank the rod in order to prevent fouling— a most undesir-
able construction in a part under compression. On the other hand,
the external rod is geometrically superior, can be made straight
and is in tension. It may be added, however, that both forms are

364 MOTOR CAR ENGINEERING

in compresBion and tension during steering, as the force applied
at the steering arm in one direction causes a thrust, and in the
opposite direction a pull in the rod according as the car is turning
to the left or to the right.

When the steering pivots are vertical, the use of pins in the tie
har are permissible, ))ut if they are angled in order to obtain easy
steering, it is necessary to use ball and socket joints. Steel tuhing,
with the ends screwed in and pinned or brazed (preferably the

STEERING GEARS 865

former), makes a satisfactory and light construction, but it is
desirable that some form of adjusting gear is provided, as sooner
or later some " set *' in the gear is bound to take place and require
rectifying. This may be corrected by elongating or jumping up
the rod, but is hardly so ready or so accurate a method as a special
form of adjustment, such as is seen in Fig. 62. All pins, ball
joints and surfaces should be case hardened in^ order to increase the
wearing qualities of the parts at which motion takes place, and
they should be protected by leather casings filled with grease, on
account of their exposed position and the detrimental effects of
wear in the steering. Slackness at any of the steering connec-
tions necessitates the continual attention of the driver to the
steering.

The necessity of fitting adequate means to prevent the
possibility of pins from slacking back need hardly be emphasised.

Buffer springs are usually employed on the ends of the steering
rod in order to reduce the vibration transmitted to the steering
wheel due to road shocks. Various forms are employed and are
fitted in conjunction with ball and socket joints, the latter being
required to allow for the movement of the steering lever in a
horizontal or approximately a horizontal plane, and of the lever
on the steering column in a vertical plane. Generally, one
spring only is placed on each end, the position being such that
shock in either direction is taken up but in some designs both
springs are fitted at one end on opposite sides of the ball. It is
usual to crank both the steering levers and the actuating lever,
partly because of the improved appearance, partly to give
straighter leads to the rods actuating them, partly because of
the particular construction employed, and partly in order to afford
ample clearances between fixed and moving parts. The method
of attachment to the stub axles varies slightly with the form of
axle pivot, but in general, a pin formed on the end of the lever
passes through the stub axle, and is secured by a castle nut at the
back. In all cases it is desirable to fit a key or feather s so as to

•if

prevent rotation, and this is essential when the levers are cranked.
In A few designs a single forging suffices for both the steering
and actuating levers on the offside of the car, but where two
separate levers are fitted it is usual to attach the steering arms
to the lower end of the stub axle. The actuating lever should
be fixed, so that its motion on either side of the centre line

366 MOTOR CAR ENGINEERING

is eqaally distributed from fall lock of one wheel to full lock of

the other.

218. Steerii^ Colcmiu. — The steering gear may be operateJ
either by worm and sector or by screw and nut, but the (ormer

STEEBING GEARS 367

is the much more extensively employed. The worm, or thread, is
mounted upon the hollow shaft passing up to the steering wheel,
but the thread may be formed on the shaft itself, although this is
unusual in any excepting solid shafts, and these are rarely seen
in modern work. The column usually serves to convey the rods
or tubes actuating the throttle and ignition levers, if hand control
is provided, and the rods may extend right through to the bottom
of the column (the usual construction) or threads may be formed
upon them which move a nut sliding in the interior of the casing
through the metal of which trunnions pass to levers pivoted on
the exterior (see Fig. 162, Vol. I.). The angular movement of
these levers is limited by stops, one arrangement of which is seen
in Fig. 65, while stops fitted to limit the movement of the steer-
ing wheel are shown in Fig. 66. It is very desirable to place
these fittings as near to the source from whence motion is desired
as possible.

In order to increase the life of the steering gear where a worm
and sector type of gear is fitted, the sector is often made of
greater length than the working length, occasionally a full wheel
being fitted. This enables one to turn the sector round to a
fresh portion of the circumference when wear takes place. It
will be clear that such is not possible in the case of a screw and
nut type, because the wearing surface is over the full length of
the nut.

In all cases the sector should be separate from the actuating
shaft so as to facilitate renewal and because the sector is of
bronze, and the lever of steel. Thrust on the worm should be
preferably taken up on ball-bearings, and since it acts in toth
directions alternately, two will be required. Often, however, only
one set is fitted, and in some designs hardened steel surfaces
are used. But good non-wearing surfaces are essential, in order
to reduce lost motion. For the sector, it is generally sufficient to
rely upon the sides of the boss upon the casing since the end
thrust on this part is not very high. Means of adjustment of the
worm may be dispensed with if ball races or hardened rings are
fitted on both sides of the worm, but if thrust is taken up in this
manner, on bne side of the worm only, some device for taking up
wear must be provided.

The casing, which is mounted directly upon the frame, is almost
universally split down the centre for facility in dismantling and

368 MOTOR CAR ENGINEERING

examination, the two halves being secured together by bolts.
Bearings shoald be amply large, and the means of lubrication
sufficient. Preferably, the actuating mechanism should be encased
in grease to ensure the efficient lubrication of the part and the
exclusion of grit.

The angular movement of the steering wheel is usually about
four times that of the road wheel. Too great a movement is to
be avoided on account of the necessity for one to be able to put
the wheels into the desired position of lock as quickly as possible,
while, on the other hand, too small a movement results in very
sensitive steering and requires a greater effort to move the
wheels. To find the velocity ratio of the gear, let n be the
number of threads on the worm and N the number of teeth in
the wheel, Ig the length of the lever on the steering sector and !«
the length of the actuating lever on the axle. Then the angular
movement of the road wheel is to the angular movement of the
worm wheel as Ig is to 1^, and the angular movement of the worm
wheel is to the angular movement of the steering wheel as 71 is
to N. Hence, the angular movement of the road wheel is to the
angular movement of the steering wheel as nZ,is to Nl^, that is —

Road wheel angle _ id^
Steering wheel angle Nl,/
Therefore, if the ratio of the two movements and the lengths of
the levers are known, the ratio of the worm gear can be ascer-
tained.

Thus, if this ratio is J, 1„ = 6 in. and 1, = 9 in.

1 __ V X 9

4 N X 6

n __ 1
N 6
so that if a 3 -start worm is employed, the complete wheel should
have 18 teeth ; small numbers of teeth are not a great disadvan-
tage here, because the question of efficiency does not enter largely
into the matter.

APPENDIX

TABLE XVII.— Areas of Circles, Advancing by IOths.

•

Areas.

•0

-1

•2

•3

■4

•5

•6

-7

•8

-9

•0

-0078

•0314

•0706

•1256

•1963

•2827

•3848

•5026

-6361

•7854

•9503

11309

1-3273

15393

1-7671

2-0106

2^2698

25446

2-8352

31416

3-4636

38013

4-1547

45239

4-9087

5-3093

67255

61575

6-6052

7-0686

7-5476

80424

8-5530

9^0792

9-6211

10-1787

107521

11^3411

11-9459

12-5664

13-20^25

13-8544

14-52*20

15-2063

15-9043

16-6190

17-3494

18-04»51

18-8574

19-6350

20-42S2

21-2372

22-0618

22-9022

23-7583

24-6301

26-5176

26-4208

27-3397

28-2744

29-2247

301907

;n-i7-25

32- 1699

33-1831

34-2120

35-2566

36-3168

37-3928

38-4846

39-59-20

40-7151

41-8539

430085

44-1787

45-3647

46-5663

#7-7837

49-0168

50-2656

51-5300

52-8102

54-1WJ2

55-4178

56-5471

58-0881

59-4469

60-8213

62-2115

63-6174

65-0389

66-4762

67-9292

69-3979

70-8823

72-3824

73-8982

75-4298

76-977«

78-5400

80-1186

81-7130

83-3230

84-9488

86-5903

88-2475

89-9204

91-6090

93-3133

05-0334

96-7691

98-5205

100-287

102-070

103-869

105-683

107-513

109-359

111-220

113097

114-990

116-808

118-8-23

120763

122-718

124-690

126-677

128-679

130-698

132-732

134-782

136-848

138-P-29

141^026

143-139

145-267

147-411

140-571

151747

153-938

156-145

158-368

160-6i»6

162-860

165-130

167-415

169-717

172-034

174-366

176-715

179079

181458

183-854

186-265

188-692

191-134

193-503

196-067

108-556

201-062

203-583

206120

208-672

211-241

213-825

^16-4-24

219-040

2-21-671

224-318

226-980

229-658

232-352

235-062

237-787

240-528

243-285

246-057

248-846

•251-650

254-469

257-304

260125

9«J-022

265-905

2t«-803

•271-716

274-646

277-591

280-552

283*529

286-521

289-529

25>2-r>53

295-593

298-648

301-719

304-805

307-908

311-026

314-160

317-309

320-474

322-»)55

326-852

330064

333-292

336-536

339-795

343-070

346-361

349-667

352-900

356-328

350-681

363-051

366-436

360-837

373-253

376-685

380-133

383-597

387-076

390-571

394-082

397-608

401150

404-708

408-282

411-871

415-476

419-097

422-733

426-385

430-053

433-737

437836

441-151

444-881

448-1528

452-390

456-168

459-961

463-770

467-595

471-436

475-292

479164

483-052

486-955

49C-875

494-809

498-760

502-726

506-708

510-706

514-719

518-748

522-793

526-854

2«

530-930

535-022

539-129

543-253

547-392

551-547

555-717

559-903

564-105

568-323

572-556

676-806

5«l-070

585-^50

589-646

593-951

598-286

602-629

606-988

611-363

615-753

620-159

624-581

629-019

633-472

637-941

642-4-25

646-926

651-442

655-973

660-5-21

665*084

669-663

674-258

678-868

683-494

688-136

692-793

697-466

702-155

706-860

711-580

716-316

721-067

725-835

730-618

735-417

740-231

745061

749-907

754-769

759-646

764-539

769-448

774-372

779-313

784-268

789-240

794-227

799-230

804-249

809-284

814-334

819-399

824-481

329-578

834-691

839-820

844-964

850-124

ass-soo

860-492

865-699

870-927

876- ito

881-415

886-685

801-970

867-272

902-589

907*922

913-270

918-635

924-011

'>29-4JP

934-822

940-249

946-692

951-150

956-625

962-115

967-620

973-142

978-679

984-231

989-800

995-384

1000-98

1006-150

1012-23

1017-87

1023-54

1029-21

1034-91

1040-63*!

1046-34

1052-00

1057-84

1063-62

1069-40

1075-21

1081-03

1186-86

1092-71

1098-58

1104-46

1110-36

1116-28

1122 21

11-28-15

1134-11

1140-09

1146-08

1152-09

115811

116415

1170-21

1176-28

1182 37

1188-47

1194-59

1200-72

1206-87

121304

1219-22

1225-42

1-231 •OS

1237-86

1244 10

1250 36

1256-64

1262-93

1-269-23

1275-56

1281-89

1288-25

129462

1301-00

1307 40

1313-82

M.C.E.

B ])

Table XVII.-

-A BE AS

OF CiBGLBs, Advancing by

IOths-

-continued.

Areas.

•0

-1 -2

•3

•4

*tf

•9

41 lSdO-25

1326-70

1333-16

1339 G4

134614

1352-65

1350*18

1365-72

1372-83

1378-85

1885-44

1392*05

1398-67

14C5 30

1411-96

1418-62

1425*31

143201

1438 72

1445*45

1452-20

1458 96

1465-74

1472-6.-J

1479-34

148617

141»301

1499-87

150674

1513-62

1520 53

1527-46

153438

154133

1548 30

1555-28

1562-28

1569-29

1576*32

1583-37

1590*43

1507-51

1604 60

161171

1618-83

1625-97

163312

1640-30

1647*48

1654-68

1661 90

166013

1676 h8

1683-65

1690-93

1698-23

1705-54

1712-87

1720 21

1727 67

1734^

1742 33

1749 74

1757 16

1764-60

1772-05

1779 52

178701

1794-51

180202

1809-56

1817 10

1824 67

1832-25

1830 84

1H47 45

185508

lhe272

1870 38

1878*05

1885 74

1893-45

11HH17

1908-90

1916-45

1924 42

1932-20

194000

1947 82

1955-65

1963-50

197136

1979^23

198713

199604

2002 96

2010*90

2018-86

2026-83 -2034 82

S042'82

2050-84

2068*87

2066-92

2074*99

21*307

200117

S099-28

2107 41 '2115 56

2J23-72

2131-89

2140 08

2148^

2156 51

2164-75

217301

2181-28

2189*56 2197-87

220(5-18

2214-52

2222-b7

-2231-23

2239-61

224801

2256-42

2264-85

2273^9

22H 75

2200^22

2298-71 1 2307-22 1

2315-74

9324-28

2332 82

2341-40

2349*96

2358 58

2367*£0

237513

«3f4-48

y393 14

2401-82

2410 ;4

24h>*22

2J27-95

2436*60

2445 45

'2454-22

346.3-01

2471-81

2480-63

24W)-47

249S32

2507-10

2516*07

2524*97

9583-88

2542-81

2551-76

2560-72

•2569-70

2578-69

•2587-70

•2596-72

2605-76

2614-12

2623-89

2638 -€8

264208

2651 -ao

2660^

2t-69 48

2678-65

26h7b3

2697-08

2706*24

2715*47

2724-71

2733 97

2743-25

2752-54

2761-85

277117

2780*61

2789-86

2799*23

2806-68

2818*08

2827 44

2836 87

2816-32

2856-78

2865*26

2874 76

2884-26

2893*79

2903*34

9918 89

61 2993-47

2932-06

2041-66

295128

2960-92

2970 57

2960-24

9980*93

2999 63

3009-31

6i2

3019-07

3028 82

3038 58

304»-36

3058-15

3067*96

3077-79

3067*63

3097 49

3107 96

3117 25

312715

3137 07

3147-01

3156-96

3166 i)2

3176*91

3186*90

3196-92

3206-95

3216-09

3-227 -05

3237-13

3247^

3267 33

3267-46

3277 69

3267*75

3297^

3306-11

3318-31

3328-63

3338-76

334001

3359-28

3369-56

3379-85

3390-17

3400-49

3410*84

3421-20

3431-57

3441-96

3452-37

3462-79

3473-23

3483-68

3494 16

3604-64 :^1514

3525-66

3536-19

3546-74

3557*80

3567-t8

3578-47

35t9-08

,8500-71

3610*35 ■ 3631*01

3631-68

3642-37

365308

366ii-80

3674-64

3685-29-

3696-06

3706-84

H717-64

3728*46

3739-28

3750-13

3760*99

3771^7

3782-76

3793-67

3801*60

3615*64

3826*60

3837*47

3818-46

3850*46

3670*48

3881-51

3892-56

3908-63

3014*71

3925*88

3936*92

3248-06

3959-20

3970-36

3981-53

S992-73

4003*93

4015-16

4026-40

4037-65

404802

4060-21

4071-51

4082-K3

4094-16

4105-51

41H5*h7

4128-25

4139-65

4151*06

4162*49

4173-93

73 . 4185-39

4196-67

4208-06

4219-86

4231-38

4242-92

4254-48

4266*04

4277-63

4289-23

4300-85

4312-48

4824-12

4335-79

4347-47

4359-16

4370-87

4382*eO

4394*34

4406-10

4417 S7

4420-66

4441-46

4453-28

4465-12

4476-97

4488-84

4500-72

4512-62

4524*54

4636-47

4548-41

4560-37

4672-35

4584-35

4596-35

4608-38

4620*42

4(32-47

4644*»1

4656-63

4W8-73

4680-a')

4692-99

470514

4717-30

4729-49

4741*68

4753-96

4766*12

4778-H7

4790-t53

4802-90

4815-20

4827-50

4830-83

485216

4864-52

4876*89

4889-27

4^1-68

4914-09

4926-5:i

4938-98

4951-44

4963-92

4976-42

49^8*93

5001-45

5014-00

5020 50

503913

5051-72

506.1-32

6076-95

5080-58

5102*24

5114-90

5127*59

5140-29

515300

5165-74

5178-48

5161-25

520402

5216-82

5229-6:)

5242*45

5255*29

5868-15

5281-02

5293-91

5306-82

5319-74

5332-67

5345-62

5358-59

5371*57

5384-57

5897-50

5410-62

5423-66

5436-72

5449-80

5462-80

547600

5480-12

5502-26

6515*42

5698*50

5541-78

5554-98

5568-20

5581-43

5594-68

5607-95

5621*23

5634-53

5647*84

566117

5674-51 1 5t87-87

5701-25

5714-64

572804

5741-47

5754-90

5768-36

5781-83

5795*31

5808-81

5R22-33

5835-86

5849-41

6862-97

5876-55

5800-15

6008-76

6917*39

5831-03

5944-60

6958-36

5972-a'5

49aV76

5999-48

6013-21

6026-97

6040*73

6054-52

6068*39

6082-13

6095-90

6100-81

6123-67

6137-55

6151-44

6165-35

6170-28

6193-^^

6907*18

62-21-15

6235-14

6249-14

6263-16

6277-19

6291-20

6305-31

6310-39

6KW-49

6347-61

6361-74

6375-88

6390-O4

6404-22

6418*41

6432-62

6446-84

6461*08

6476*34

6480-61

6503-80

651819

6532-51

6546-85

6661-20

6575-56

6589*94

6604*34

6618-75

6633-18

6647-62

6662-08

6676-55

6691-05

6705-55

6720*07

6734-61

674916

6763-73

6778*32

6702-92

6807-54

6822-17

fKii5-82

6851-48

6866-16

6880-a5

6805*56

6910-29

6925-03

6939-79

6964 -5(!

(i969-35

C98416

6098-98

7013-81

7028-67

7043-53

7058*42 1 7073*33

7088-23

71C816

711811

7i:«-or

7148-05

716304

7178*05

710307

7208 11 , 7223 17

7238-24

7253 33

7-268 43

7283-55

7298-69

7313-84

732900

7344 18

7350-38

7374-50

7389-82

7405 07

7420 33

7435-60

7450-90

7466-20

7481-53

7496-87

7512*22

7527*69

7542-98

7558 38

7573-80

7580-23

7604*68

7620-14

76:J5*62

765119

7666 63

7682*16

7697-70

7713 26

77-28 83

7744-42

776003

7775 65

7701-29

7806-94

7822*61

7638*29

100

7854 00

7860-71

7885-44

7901-19

7916-95

7932*73

7948*53

7964-34

'i 980*16

7P96-00

APPENDIX

Table XVIII.— Cibcumferencbs op Circles.

Circumference!?.

DiAm

B. W iCVi^X •

•0

•I
•31

•2

-3

-94

-4
1-25

•5
1-57

-6

1-88

-7
2-19

•8

-9

•00

•62

2-51

2-82

314

3-45

3-77

4-08

4-39

4-71

5-02

5-34

5-65

5-96

«-28

6-59

6-91

7-22

7-53

7-85

8^16

8-48

8-79

9-11

9-42

9-74

1005

10-36

10*68

10-99

11-30

11-62

11-93

12-25

12 56

12-88

13-19

13-50

13-82

1413

14-45

14-76

15-08

15-39

•0

15-70

16-02

16-33

M-65

16-96

17-27

17-59

17-90

18-22

18-53

(')

18-84

19-16

19-47

19-79

2010

20-42

20-73

21-04

21-36

21-67

21-99

22-30

22-61

22-93

23-24

2356

23-87

24-19

24-50

24-81

2513

25-44

25-76

26-07

26-38

26 70

27-01

27-33

27-64

27-96

28-27

'28-58

28-90

29 21

29-53

29-84

30-15

30-47

30-78

31-10

31-41

31-73

32-04

32-35

32-67

32-98

33-30

3.3-61

33-92

31-24

31-55

34-87

35-18

H5-50

35-81

3612

36-44

36-75

3707

37-38

37-69

38-01

38-32

38-64

38-95

39-27

39-58

39-89

40-21

40-52

40-84

41-15

41-46

41-78

4209

42-41

42-72

43-03

43 35

43-66

43-98

44-29

44-61

44-92

45-23

45*55

45-86

46-18

46-49

46-80

4712

47-43

47-75

4806

48-38

48-69

49-00

49-32

49-63

49-95

50-26

50-57

50-89

51-20

51-52

61-83

52-15

5246

52-78

53-19

53-40

5372

54-03

54-35

54-65

54-97

55-29

55-60

55-92

56-23

56-64

56-86

57-17

57-49

57-80

5811

58-43

58-74

59-06

59-37

59-69

60-(K)

60-31

60-63

60-94

61-26

61-57

61-88

62-20

62-51

6283

6314

63-46

63-77

64-08

64-40

•

64-71

6503

65-34

65-65

65-97

66-28

66-60

66-91

67-22

67-54

67-85

68-17

68-48

68-80

69-11

69-42

69-74

70-05

70-37

70-68

7100

71-31

71-62

71-94

72-25

72-57

72-88

7319

73-51

73-82

74-14

74-45

74-76

75-08

75-39

75-71

76-02

76-34

76-65

76-96

77-28

77-59

77-91

78-22

78-54

78-85

79-16

79-48

79 79

80-11

80-42

80-73

81-05

81-36

81-68

81-99

82-30

82-62

82-93

83-25

83-56

83-88

84-19

84-50

84-82

8513

85-45

85-76

86-07

8(i-39

86-70

87-02

87-33

87-65

87-96

88-27

88-59

88-90

89-22

89-53

89-84

9016

90-47

90-79

91-10

91-42

91-73

92-04

92-36

92-67

JI2-99

93-30

93-61

93-93

94-24

94-56

94-87

95- 19

95-50

95-81

96-13

96-44

96-76

97-07

97-38

97-70

98-01

98-33

98-64

98-96

99-27

99-58

99-lM)

100-2

100-5

100-8

1011

101-4

101-7

102-1

102-4

102-7

103-0

103-3

103-6

103-9

104-3

104-6

104-9

105-2

105-5

105-8

106-1

106-5

106-8

1071

107-4

107-7

108-0

108-3

108-6

109-0

109-3

109-6

3r>

109-9

110-2

UO-5

110-8

111-2

111-5

111-8

112-1

112-4

112-7

3<i

113-0

113-4

113-7

U4-0

114-3

114-6

114-9

115-2

115-6

115-9

116-2

116-5

116-8

117-1

117-4

117-8

118-1

118-4

118-7

119-0

119-3

119-6

1200

120-3

120-6

120-9

121-2

121-5

121-8

122-2

3S)

122-5

122-8

123-1

123-4

123-7

124-0

124-4

124-7

125-0

125-3

125-6

126-9

126-2

126-6

126-9

127-2

127-5

127-8

128-1

128-4

128-8

129-1

129-4

129-7

130-0

130-3

130 6

131-0

131-3

131-6

131-9

1322

132-5

132-8

133-2

133-5

133-8

1341

134-4

1.34-7

135-0

135-4

135-7

136-0

136-3

136-6

136-9

137-2

137-6

137-9

138-2

138-5

138-8

1391

139-4

139-8

140-1

140-4

140-7

141-0

141-3

141-6

142-0

142-3

142-6

142 9

143-2

143-5

143-9

144-2

144-5

144-8

145-1

145-4

146-7

1460

146-3

146-7

147-0

147-3

147-6

147-9

148-2

148-5

148-9

149-2

149-5

149-8

1501

150-4

150-7

1511

151-4

151-7

152-0

152-3

152-6

152-9

153-3

163-6

153-9

154-2

154-5

154-8

155-1

155-5

155-8

156-1

156-4

156-7

1570

157-3

167-7

158-0

158-3

158-6

158-9

169-2

159-5

159-9

B 2

APPENDK

Table XVIII. — Circomfebences of Cibcles — eontinued.

Circumferences.

Diaiu. _

•

•0

•1

•2

160-8

•3
161-1

-4

161-4

•5
161-7

•6

-7
162-4

-8

•9

160-2

160-5

162-1

162-7

1630

163-3

163-6

163-9

164-3

164-6

164-9

165-2

165-5

165-8

166-1

166-5

166-8

1671

167-4

167-7

1680

168-3

168-7

169-0

169-3

169-6

169-9

170-2

170-5

170-9

171-2

171-5

171-8

1721

172-4

172-7

1731

173-4

173-7

174-0

174-3

174-6

174-9

175-3

175-6

5<j

175-9

176-2

176-5

176-8

177-1

177-5

177-8

178-1

178-4

178-7

1790

179-3

179-7

1800

180-3

180-6

180-9

181-2

181-5

181-9

182-2

182-5

182-8

183-1

183-4

183-7

1840

184-4

184-7

185-0

185-3

185-6

185-9

186-2

186-6

186-9

187-2

187-5

187-8

188-1

188-4

188-8

1891

189-4

189-7

1900

190-3

190-6

191-0

191-3

191-6

191-9

192-2

192-5

192-8

193-2

193-5

193-8

194-1

194-4

194-7

195-0

195-4

195-7

196-0

196-3

196-6

196-9

197-2

197-6

197-9

198-2

198-5

198-8

199-1

199-4

199-8

2(K)-1

2(M)-4

200-7

2010

201-3

201-6

202-0

202-3

202-6

202-9

203-2

203-5

203-8

204-2

204-5

204-8

205-1

206-4

205-7

206-0

206-4

206-7

207-0

207-3

207-6

207-9

208-2

208-6

208-9

209-2

209-5

209-8

2101

210-4

210-8

2111

211-4

211-7

212-0

212-3

212-6

213-0

213-3

213-6

213-9

214-2

214-5

214-8

2151

215-5

215-8

216-1

216-4

216-7

2170

217-3

217-7

218-0

218-3

318-6

218-9

219-2

219-5

219-9

220-2

220-5

220-8

22M

221-4

221-7

2221

222-4

222-7

223-0

223-3

223-6

223-9

224-3

224-6

224-9

225-2

225-5

225-8

2261

226-5

226-8

227-1

. 227-4

227-7

228-0

228-3

228-7

2290

229-3 229-6 |

229-9

230-2

230-5

230-9

231-2

231-5

231-8

2321

232-4

232-7

2331

233-4

233-7

234-0

234-3

234-6

234-9

235-3

235-6

235-9

236-2

236-5

236-8

237-1

237-5

237-8

2381

238-4

238-7

2390

239-3

239-7

240-0

240-3

240-6

240-9

241-2

241-5

241-9

242-2

242-5

242-8

243-1

243-4

243-7

244-1

244-4

244-7

245-0

245-3

245-6

245-9

246-3

246-6

246-9

247-2

247-5

247-8

2481

248-5

248-8

2491

249-4

249-7

2500

260-3

250-6

2510

251-3

251-6

251-9

252-2

252-5

252-8

253-2

253-5

253-8

264-1

254-4

254-7

255-0

255-4

255-7

2560

256-3

256-6

266-9

257-2

257-6

257-9 258-2

258-5

258-8

259-1

259-4

259-8

260-1

260-4

260-7

261-0 261-3

261-6

262-0

262-3

262-6

262-9

263-2

263-5

263-8

264-2

264-5

264-8

265-1 265-4

265-7

266-0

266-4

266-7

267-0

267-3

267-6

267-9

268-2 268-6

268-9

269-2

269-5

269-8

2701

270-4

270-8

271-1

271-4

271-7

272-0

272-3

272-6

273-0

273-3

273-6

273-9

274-2

274-5

274-8

275-2

275-5 275-8

2761

276-4

276-7

2770

277-4

277-7

278-0

278-3

278-6

278-9

279-2

279-6

279-9

280-2

280-5

280-8

281-1

281-4

281-8

2821

282-4

282-7

283-0

283-3

283-6

2840

284-3

284-6

284-9

285-2

285-5

285-8

286-1

286-5

286-8

287-1

287-4

287-7

288-0

288-3

288-7

289-0

289-3

289-6

289-9

290-2

290-5

290-9

291-2

291-5

291-8

2921

292-4

292-7

2931

293-4

293-7

2940

294-3

294-6

294-9

295-3

295-6

295-9

296-2

296-5

296-8

297-1

297-5

297-8

298-1

298-4

298-7

3990

299-3

299-7

300-0

300-3

300-6 1 300-9

301-2

301-5

301-9

302-2

302-5

302-8

303-1

303-4

303-7

304-1

304-4

304-7

3050

305-3

305-6

305-9

306-3

306-6

306-9

307-2

307-6

307-8

3081

308-5

308-8

309-1

309-4

309-7

3100

310-3

310-7

3110

311-3

311-6

311-9

312-2

312-5

312-9

213-2

313-5

313-8

100

314-1

314-4

314-7 3151

315-4

315-7

316-0

316-3

316-6

316-9

APPENDIX

Table XIX.— Cibcumfergnciss and Areas of Circlrs kbom ^ ia. to 5^{ in.

Uia.

r«

Circum.

Area.

Dill.

Circnm.

Area.

Dia.

Circiim.

Area.

Dia.

Circum.

Area.

•0981

•2945

•3927

•4908

•589

•6872

•7854

•8885

•9817

1-0799

M781

1^2702

1-3744

^4726

1-5708

1-6689

1-7771

1-8653

1-9635

20616

2- 1598

2-258

2-3562

2-4543

2-5525

2-6507

2-7489

•00077

•00307

•0069

•01227

•0192

•02761

•0376

•04909

•0621

•0767

•0928

•1104

•1296

•1503

•1725

•1963

•2216

■2485

•2768

•3068

•3382

•3712

•4057

•4417

•4793

•5185

■5591

•6013

'ff

2847

2-9452

3-0434

31416

33379

3-5343

3-7306

3-927

4-1233

43197

4-516

4-7124

4-9087

5-1051

5-3014

54978

5-6941

5^8905

6-0868

6-2832

6-4795

6-6759

6-8722

7-0686

7-2649

7-4613

7-6576

7-854

-645

■6903

•"737

-7854

•8866

•994

M075

12271

1353

r4848

16229

1767 1

19175

20739

2-2365

24052

2-58

2-7611

29483

31416

33410

35465

3^7584

3-976

4-2

44302

4-6 i64

4-9087

m
n

8^0503
82467
8-443
8-6394
8-8375
9-0321
9-2284
9-4248
9-6211
9-8175
10-014
10-21
10-406
10-602
10-799
10-995
11191
11-388
11-584
11-781
11-977
12173
12369
12566
12-762
12-959
131.55
13-351

51573
54119
56723
5-9395
6-2126
6-4918
6-7772
7-0686
73662
7^6699
7-9798
8-2957
8-618
8-9462
9-2807
9-6211
9-968
10-32
l(f-679
11-044
11-416
11-793
12177
12-566
12962
13364
13-772
14^186

13-547
13-744
13-94
14137

14333

14-529

14-725

14-922

15119

15-315

15-511

15^708

15-904

161

16-296

16493

16689

16-886

17-082

17-278

17474

17671

17-867

18-064

18-261

18^457

18653

14606

15033

15-465

15904

16-394

168

17257

1772

18-19

18-665

19-147

19-635

20129

20-629

21135

21-647

21166

22^69

23221

23758

24-301

24-85

25-406

25967

26535

27108

27-688

Table XX.— Dkcimal Fractions op a Lineal Inch in Milltmetres.

Inches.

Mm.

Inches.
•21

Mm.
5-334

I Inches.

Mm.

Inches.
•61

Mm.
15-494

Inches.

Mm.

•01

•254

' -41

10-414

•81

20-574

•02

•508

•22

5-588

•42

10-668

•62

bV748

1 ^82

20-828

•03

•762

•23

5-842

•43

10-922

•63

16002

•83

M *. V t.- ••

•04

1016

-24

(5-096

•44

11-176

•64

16-256

•84

21-336

•05

1270

■25

(;-350

•45

11-430

•65

16-510

•85

21-590

•06

1-254

■26

6-604

•46

11-684

■66

16764

-86

21-844

•07

1-778

•27

6-858

•47

11-938

•67

17018

1 -87

22098

•08

2^032

•28

7112

•48

12-192

•68

17-272

1 ^88

22-352

•09

2-286

•29

7-366

•49

12-446

•(>9

17-526

•89

22-606

•10

2-540

•30

7-620

•50

12-700

•70

17-780

•90

22-860

•11

2-794

•31

7-874

•51

12-954

•71

18034

, '^1

23114

•12

3-018

•32

8-128

r>2

13-208

•72

' 18-288

' 92

23-368

•13

3-302

•33

8-2H2

•53

13-462

•73

18-542

•93

23622

•14

3-556

•34

8-636

-54

13-716

•74

18-796

•94

23^876

•15

3-810

•35

8-890

•55

13-970

•75

19050

•95

24130

•16

4064

•36

9114

•56

14-224

•76

19-304

1 -96

24-384

•17

4-318

•37

9-398

1 ^57

14-478

•77

19-558

•97

24-638

•18

4-572

-38

9-652

•58

14-732

•78

19-812

•98

24-892

•19

4-826

•39

9-906

•59

14-986

-79

20-066

■99

25-146

•20

5-080

•40

10-160

•60

15-240

•80

20-320

1-00

25-400

APPENDIX

Table XXI. — Inches anh Fractions with Millimetre Equivalents.

In.

Um.

1
In.

Mm.

In.

1
Moi..

In.

Mm.

In.

Mm.

•79

38-89

3.^

76-90

11509

153-19

1-58

39-68

77-78

4ft

116-68

6ft

153-98

2-38

40-48

78-58

4JS

116-68

<JA

154-78

317

41-27

79-37

117-47

156-67

3-93

42-06

8016

118-26

156-36

4-76

42-66

3ft

80-96

119-C6

63"«

157-16

6-55

43-65

3^3

81-75

483

110-86

63^

157-95

6-34

44-44

82-54

120-64

168-74

7J4

185

45-24

"'3 a

83-34

48§

121-44

6:ft

159*54

7-98

46-03

3ft

8413

122-23

6ft

160-33

8-73

183

46-83

m .

84-93

4§S

123-03

16113

fl-52

47-62

86-72

123-82

161-02

il3

10-31

188

48-41

86-51

438

124-61

162-71

11 11

49-21

h'a

S7-31

126-41

6ft

163*51

iiS

11-90

185

5)00

3i§

6810

126-20

6^3

164-30

12-69

CO-79

88-89

126-90

16609

13-49

61-59

89-60

127-79

165-89

14-28

62-38

^^.

90*18

5ft

128-53

6ft

166-68

i§

16-C8

63-18

91-28

129-38

6j;8

167-48

15-87

53-97

9207

130-17

168-27

ii^

16-66

64-76

92-86

130-96

169-06

17-46

65-56

93-66

5ft

131-76

6fi

160-86

§e

18-25

56-35

383

94-46

59^a

132-65

683

170*65

19-04

57-14

95-24

133-34

171-44

§S

19-84

2rPa

57-1)4

96-04

134-14

683

172*24

20-68

68-73

3J8

96-83

6A-

134*93

6^8

173*03

21-43

2|i

59-53

97-63

135-73

173-83

22-22

60-32

98-42

136-52

174*62

2301

61- J 1

388

99-21

513

137*31

688

175-41

23-81

2A'

ei-91

3j5

100-01

5ft

138-11

6^8

176-21

24-eo

2JS

62-70

38^

190-EO

5A8

]38-i)0

63i

177*00

25-89

63-49

101-59

139*69

177*79

26-19

2a?

64-29

4.A

102-39

5i3

140-49

178-39

26-98

2ft

65-08

103-18

5ft

141-28

7ft

179-38

27-78

2A8

66-86

4:fli

103-96

5i5

142-06

180-18

28-67

66-67

104-77

142-87

180*97

29-36

2!^i

t7-J6

105-56

5§i

143-66

7.^.

181-76

30-16

2*i

68-26

4 A

106-36

5}i

144-46

7ft

182-56

Is'a

30-95

28§

0305

4:;.

10716

583

145-25

7^a

183-35

31-74

69-84

107-94

14604

184-14

32-54

285

70-64

^^'i

108-74

583

146-84

184-04

33-33

71-43

4ft

1C9-03

147-63

7ft

185-73

34-13

72-23

110-33

148-43

7ii

1&6-53

34-92

73-02

11112

149-22

187-32

iA§

36-71

73-81

111-91

588

160-01

7J3

188-11

36-51

2}5

74-61

4ft

112-71

5}8

150-61

7ft

188*91

li§

3730

2§i

75-40

4.^,5

113-50

5S5

151 -CO

7JS

189-70

38-09

761l>

114-29

t 6

162-39

100*49

APPENDIX

Table XXI.— Inches and Fractions with Milliiiktre

Equ I valents — continued.

Id.

Mm.

In.

7*5

7§i

7JA

7«

7|5

7}3

m
m

731
8

8^1
83V
«A

8i
85^1

8*i

8,^1,

8*8

8*J

8*!

88i

8}S

8fl3

«3

Hii9

8i3

8|}

88!
818

191*29
192-06
192-88
193-67
194-46
195-26
196*05
196-84
107*64
198-43
199*23
200-02
200-81
201-61
202-40
203-19
201*99
204-78
205*57
206-37
207*16
207-96
208-75
209-55
210*34
21113
211*92
212-72
213-51
214-31
21510
215-90
216-60
217-48
218-27
219-07
219-66
220*66
221-45
222-25
223-04
223-83
224-62
225-42
226*21
22701
227*80
2-28-59

9^7

Sill

9ii

9*9

9^«

9ii
m
m

9i
985

m
93

9*3
934
10

lOA

m^
10|

lOA
lOrl,
lOA
lOi

lOA
lOA
10*J
101
10*1
lO/fl

io*S
10.5

Mm.

22939
230-18
230*97
231*77
232-56
233-36
234-15
231*95
235-74
236*53
237-32
23812
238-91
239-71
240-30
2U-30
212*09
212-88
213-67
241*47
245-26
246-06
246-85
217*65
248-44
249-23
250-02
250*82
251-61
252-41
253*23
253-99
254-78
255-J6
256-37
25717
257*96
258*76
259*55
260-35
261-14
261*93
262-72
263-52
264*31
265-11
265-90
266-70

In.

Mm.

Id.

10*3

267-49

laA

lOA

268*28

1V«

10*3

269*07

12,11 ■

log

260-87

12*

108*

270-66

12&

lOJi

271*46

12A

1089

272-25

12A

103

273-05

12J

loss

273*84

lots

274-63

12A

1083

275*42

12**

lOJ

276*22

123

1083

27701

12*3

io}8

277*81

12A

108*

278*60

12*3

279-39

12*

iiA

280-18

12*3

iiA

280-98

12A

iiA

281-77

12*3

282*57

128

HjPj

283-36

1^*

lift

281*16

12JA

iiift

284*95

1283

•235*74

123

286*53

1283

287*33

12}8

H**

288*12

1283

HiJ

288-92

12i

H*3

299-71

1283

290-51

12}8

11*3

201*30

133*

11*

292-09

11*3

292-88

13A

Hxl,

293*68

13 ,\,

11*3

294*47

13A

HiJ

285-27

13*

118*

29606

13A

H}*

206*86

13ft

11.83

297*65

13/,

206-44

13i

1185

299-23

13A

300*03

13ft

H83

300-82

134*

301*62

138

1183

302-41

13*3

H!8

303-21

13ft

Hi*

30400

13*5

304-79

13*

Mm.

In.

305-50
306-38
30718
307*97
306-76
300-56
310*35
811*14
311*04
312*73
313*53
314*32
315*11
315-91
316-70
317*40
318-29
319*08
319-88
320-67
321-46
322*26
323*05
323-84
324-64
325*43
326*23
327*02
3-27-81
328-61
320*40
33019
330-99
331-78
332-56
333-37
33416
334*96
335-75
336-54
337 34
338-13
336*93
339*72
340-51
341-31
342-10
342-89

13*3

13ft

13*3

138

138*

13**

1383
13i

1383
1313

1383

133

1383

13J8
138*
14

143^

Hft

14ft

HA
14*

HA
Hft
H**
Hg

14*1
Hft

14*3

14*

14*3

Hft

14*3

148

148*
HJS

1483

14J •

1488

14J8

1483

1488

H}g

143*

Mm.

343-60
344-48
345-28
34607
346-86
347*66
348-45
349*24
350*04
350*83
351*63
352*42
353*21
354-01
354*80
355*50
356-30
357*18
357*98
358-77
359-56
360-36
36115
361-94
362-74
363-53
364-33
365-12
365*01
366*71
367*50
368*29
369*09
369-88
370*68
371*47
372*26
373*06
373*85
374-64
375*44
376-23
37703
377-82
378-61
379-41
390*20
380-99

APPENDIX

Table XXII. — Eqi'ivalent Values of Millimetres akd Ikches.

Milli-
metres.

•

t-4

— •J

Inches,

•

Sis

?!£

Inched.

•

±1

•
K

■0394

1-6142

3-1890

121

47638

161

6-3386

•0787

1-6536

3-2284

122

4-8032

1112

6-3780

•1181

1-6929

3-2677

123

4-8426

163

6-4174

•1575

1-7323

3-3071

124

. 4-8819

164

6-4568

•1968

1-7717

3-3465

125

4-9213

165

6-4961

•2362

1-8110

' 3-3859

126

4-9607

' 166

6'53,5o

•2756

1-8504

3-4252

127

5-(X)00

167

6-5749

•3150

1-8898

3-4646

128

5-0394

168

6-6142

•3543

1-9291

3-o04(»

129

5-0788

' 169

6-6536

•3937

.50

1-9685

3-5433

130

6-1182

170

6-6930

•4331

2-0079

3-5827

131

' 5-1575

171

6-7323

•4724

20473

3-6221

132

5-1969

172

6-7717

•5118

20866

3-6614

133

5-2363

173

6-8111

•5512

2-1260

3-7008

134

5-2756

174

6-85(K5

l.">

•5906

21654

3-7402

135

5-3150

175

6-8898

•6299

2-2047

1 3-7796

136

5-3544

176

6-9292

•6693

2-2441

3-8189

137

5-3938

177

6*9686

•7087

2-2835

3-8583

138

5-4331

178

7-0079

•7480

2-3228

3-8977

139

5-4725

179

7-0473

•7874

2-3622

100

3-9370

140

5-5119

180

7-0867

•8268

2-4016

101

3-9764

141

5-5512

181

7-1261

•8661

24410

102

4-0158

142

5-5906

182

7-1654

•9055

2-4803

103

4-0552

143

5-6300

183

7-2048

•9449

2-5197

104

4-0945

144

5-6693

184

72442

•9843

2-5591

105

4-1339

145

5-7087

185

7-2835

10236

2-5984

106

4-1733

146

5^7481

186

7-3229

1-0630

2-6378

107

4-2126

147

5-7874

187

7-3623

11024

2-6772

108

4-2520

148

5-8268

188

7-4016

1-1417

2-7166

109

4-2914

149

5-8662

189

7-4410

11811

2-7559

110

4-33p7

150

5-9056

190

7-4804

1-2205

2-7953

111

4-3701

151

5-9449

191

7-5198

1-2598

2-8347

112

4-4095

152

5-9843

192

7-5591

12992

2-8740

113

4-4489

153

6-0237

193

7-5985

1-3386

2-9134

114

4-4882

154

60630

194

7-6379

r3780

2-9528

115

4-5276

155

61024

195

7-6772

1-4173

2-9922

116

4-5670

156

6-1418

196

7-7166

1-4567

3-0315

117

4-6063

157

6-1812

197

7-7560

1-4961

3-0709

118

4-6457

158

6-2205

198

7-7954

1-5354

31103

119

4-6851

159

6-2599

199

7-8.347

1-5748

3-1496

120

4-7245

160

6-2993

200

7-8741

300

11-811

500

19-685

700

27-559

9(M3

35-433

1,100 ^

43-307

400

15-748

600

23-622

800

31-496

1,000

39-370

1,200 !

47-244

APPENDIX

'II

Table XXI 1 1. — Pounds in Kilogrammes.

PoundB,

Kilogrs.

Pounds.

KilogrH.

Poumls.

KilogTH.

1
PjondH.

, 01

Rilogre.

PoimdK.

KilOgTR.

0-454

9-525

18-597

27-669

36-741

0-907

9-979

19-051

28-123

37-195

1-361

10-433

19-504

28-576

37-648

1-814

10-886

19-958

29-030

38-102

2-268

11-340

20-412

29-483

38-555

2-722

11-793 I

20-865

29-937

39009

3175

12-247

21-319

, «7

30-391

39-463

3-629

12-701

21-772

30-844

39-916

4-082

13- 154

22-226

31-298

40-370

4-536

13-608

22-680

31-751

40-823

4-989

14061

23-133

32-205

41-277

5-443

14-515

23-587

32-659

41-731

5-897

14-969

24-04(>

, 73

33112

42-184

6-350

15-422

24-494

1 74

33-566

42-638

6-804

15-876

Hi)

24-948

34-019

43-091

7-257

16-329

25-401

34-473

43-545

7-711

16-783

25-855

34-927

43-998

8-165

17-236

26-308

35-380

44-452

8-618

17-690

26-762

35-834

44-906

9-072

18-144

27-252

36-287

100

45-359

Table XXIV'.— Kilogrammes in Pounds.

Kilas.

Pounds. 1

KiloH.
21

Pounds.

KiloH.

Pounds.

KiloH.

Pounds.

Kilos.

Pounds.

2-205 '

46-297

90-389

134-482

178-574

4-409

48-502

92-594

136-486

180-779

6614

50-706

94-799

138-891

182-983

8-818

52-911

97003

141-096

185118

11-023

55115

99-208

143-300

197-393

13-228

57-320

101-413

145-505

1S9-597

15-432

59-525

103-617

147-710

194-802

8 ,

17-637

61-729

105-822

1 68

149-914

194-010

19-842

63-934

108-026

1 69

152-119

196-211

22-046

66-139

110-231

1 70

154-323

198-416

24-251

68-343

112-436

1
71

156-528

200-620

26-455

70-548 !

114-640

158-733

202-895

28-660

72-752 ,

116-845

160*937

205-330

30-865

74-957

119-049

163-142

207-234

33-069

3.)

77-162

121-254

165-347

209-439

35-274

79-366

123-459

167-551

211-644

37-479

81-571

125-663

169-756

213-848

39-683

83-776

127-868

171-960

316-053

41-888

85-905

130-073

174-165

218-275

44092

)

88-188

132-277

176-370

100

220-462

APPENDIX

Table XXV. — Pounds per Sqitarb Inch ik Eilooramhes per

Sqcabr Centimetrb.

Lb*..

KilOA.

, Lbs.

Kilos.

Lbs.

Kilos.

Lbs.

Kilos.

Lbs.

KiloH.

per
in.a

per
cm.«

per
in.s

I)er
cm. 2

I)er
in.«

per
cm.«

per
cni.«

cni.«

100

7^08

2.900

2a3^89

5.700

400-75

8.500

507-61

16.500

1160-06

aoo

1406

3.000

210*92

5.800

407-78

8,600

604*64

17.000

1196-22

300

21*09

3.100

217-95

5.900

414-81

8,700

611*67

17.500

1230-37

400

2812

3,200

22i-98

6.000

421*84

8.800

618*70

18,000

1265*53

500

3515

3.300

232^01

6,100

428-87

8,900

625*73

18,500

1300-66

600

4218

3,400

239-05

6,200

435-90

9,000

632-76

19.000

1335-83

700

4921

8.500

•21607

6.300

442-93

o.ino

630*79

10.500

1370*99

800

66^24

3,600

253-10

6.400

440-96

9.200

616-ffl

20.000

1406*14

900

63'^

8.700

26013

6,500

456-00

0.300

653-a<>

20,500

1414*29

1,000

70-31

3.800

26717

6.6G0

464-02

9,400

660-88

21,000

1476*45

1.100

77-34

3,900

274-20

6,700

471-06

9,500

667-22

21,500

1511-60

1.2Q0

84-37

4,000

281-23

6.800

478-00

9.600

674-95

22,000

1546-75

1,300

91-40

4.100

288-26

6,900

485-12

9.700

681 -OS

22.500

1581*91

1.400

98-43

4.200

29V29

7,000

492-15

0,800

080-01

'23.000

1617-06

1.500

105-46

4,300

302-32

7.100

49918

0,900

606*04

23,500

1662-21

1.600

112-49

4.400

309-35

7,200

506*21

10.000

7^13-07

24,000

1687-37

1,700

119-52

4,500

316-88

7.300

513-21

10.600

736-22

24,5'J)

1722*52

1.800

126-56

4,600

323-41

7,400

520-27

ii.roo

773-38

25.000

1757*67

1.900

133-58

4,700

330-44

7,500

527-30

11,600

806-53

25.500

1792*83

2,000

140-62

4.800

337-47

7,800

534-33

12.000

848-68

26.000

1S27-08

2,100

147-64

4.900

344-53

7,700

511-36

12,500

878-84

26,500

186313

2,200

154-67

5.000

351-53

7,800

540*39

13,000

91 8^90

27.000

1896-29

2,300

161-71

5,100

358-56

7,900

655-42

13.500

040-14

27.500

1033*44

2,400

168-74

5,200

36550

8.000 -

562-46

14.000

06430

28.000

1968*60

2,500

175-77

5,300

37263

8,100

569-49

14,500

10I0^45

28,500

2003-75

•2,600

182-80

5,400

379-66

8,200

576-52

15,000

1054-60

20,000

2038*90

2.700

189-83

5,500

386-60

8,300

683-56

15.500

1080*76

20,500

2074-06

2,H00

li»6-86

5.600

393-72

8,400

590-58

16.000

112401

30,000

2100*21

Table XXVI.— Impkrial Stand.* rd Wire (iAugb.

No.

Oiameter.

Sectional area.

1 No.

Diameter.

St^ctional aiva.

In.

Mm.

In.

Mm.

In.

Mm.

1
III. Mm.

7/0
6/0
5/0
4/0
3/0
2/0
1/0

•500
•464
•432
•400
•372
•348
•324
•300
•276
•252
-232
•212
•192
•176

12^7

ir8

110
10-2
9-4
8-8
8-2
7-6
7*0
6-4
5*9
54
49
4-5

•19(53
•1691
•1466
•1257
-1(KS7
•0951
•0824
•0707
•0598
•0499
•0423
•0353
•0290
•0243

126-69
109-09

94-56

8h07

7012

61-36 1

53-19

46-60

38^58

3218

27-27 '

22-77

18-68 '

15-70

8
9
10
11
12
13
14
15
16
17
18
19
20
21

•160
■144
•128
•116
-104
•092
•080
•072
•064
•056
•048
•040
•036
•032

4-1
3-7
33
3-0
2-6
23
20
l-S
1*6
1*4
12
10
0-9
0^8

•0201
•0163
•0129
•0106
•0085
•0066
•0050
•0041
•0032
•0025
•0018
•0013
•0010
•0008

12-97
10-51
8-30
6 82
5-48
429
324
263
207
1 rfi9
117
0-81
0-65
0-51

APPENDIX

Table XXVII.— Decimal Equivalents (Sixty-Focbths).

l-64t.h

■015625

1
17-64th8

•?65625

33-64ths

•515625

49-64ths

•766625

l-32n(l

■03125

9-32nc]8

•28125

17-32nds

•53125

25-32nd8

•78125

3-64th8

•046875

19-64ths

•296875

35.64th s

•546875

51-64ths

•796875

1-I6th

■0625

' 5- 16th 8

•3125

9-16th8

•5625

13-16th8

•8125

5-04ths

•078125

i 21-64th8

•328125

37-64tli8

•578125

53-64tha

•828125

3-32Dds

•09375

ll-32u(]s

•34375

19-32n(ls

•59375

27.32n(Ls

•84375

7-«>4ths

109375

23-6 Iths

•359375

39-64 ihM

•609375

55- 64 ths

•859375

l-8th

125

3-8ths

•375

5-8th8

•625

7-8ths

•875

l»-64th8

140625

25-6 Iths

•390625

41-64ths

■640625

57-64th8

•890625

5.32uds

15625

13-32rKl8

•40625

21-32n(ls

•65625

29-32nds

•9062S

ll.«4th8

171875

27 64ths

•421875

43.64th8

•671875

59-64ths

'921875

3-lHth8

1875

7-16ths

•4375

lM6th8

•6875

15-16ths

•9375

13-64th8

203125

29-6 khs

•453125

45-64 ths

•703125

61-64th8

•953125

7-32imIs •

21875

15-3211(18

•46875

23-32nd8

•71875

31.32nds

•96875

l5-64thB 1 ■

234375

31-6Uhs

•484375

47.64ths

•734375

63-64th8

•984375

l-4th 1 -

1-half

3-4ths

•75

Table XXVIIL— Circulau, Diametral

AND Metric Pitches.

Circular

Diametral

Circnlfir

Module.

Di imetral

Piteb.

I'iteh.

Pitch.

I'itcli.

Pitch.

1-795

• 2

1-571

1-5

16-988

1-933

1-396

1^75

14^614

2-094

J -257

12^700

ifff

2-185 ■

1142

2"25

. 11-288

2-285

1-041

2^5

10-160

2-394

•8976

2^75

9-236

2-513

•785

8^466

U'e

2-646

•6^28

3^6

7-257

2-798

•524

6-850

2-957

•449

4^5

6-644

3-142

•398

5 •

5-080

8-351

•349

5-5

4-618

3-590

•814

4-288

8-867

•286

8-628

4-189

•262

8-175

4-570

•224

2-822

5027

•196

2-540

5-585

•175

2-309

6-283

•20

•157

2-117

7-181

•143

1-8J4

8-378

•131-

1-587

10058

•121

1 2-566

•112

f'rr

16-755

•105

APPENDIX

Table XXIX. — Metric 60° Screw Threads.

Diameter

of Screw

mm.

Pitch of

ThreMdH

mm.

1^0

Core
Diameter
mm.

Area at

bottom

of Thread

mm.2

Diameter
ol Screw
mm.

Pitch of

Tlirvad

mm.

Core

Diamet<'r

mm.

20-10

Area at

bottom

of Tlirtad

mm.*

4-70

1735

-24

317-3

1^0

5^70

2552

3^0

22-10

383-6

1^0

670

3526

-27

3-0

2310

419-1

•^8

1-25

6^38

31-96

2410

456-2

1^0

7-70

46-57

-30

3-5

25-45

508-6

125

7^38

42-73

3-5

27^45

592-0

*10

1-5

8^05

50-89

-33

3-5

28-45

635-6

-11

1-5

9-05

64-25

3-5

29-45

681-0

1-5

10-05

79-32

-36

4-0

30-80

7451

*12

1-75

9-73

74-22

32-80

844-96

-14

2^0

11-40

10207

-39

4-0

33 80

897-3

*16

2^0

13-40

141-03

34-80

951-2

1-5

1405

155-50

*42

4-5

36-15

1027-0

-18

2^5

14-75

171-21

38-15

11430

1-5

1605

202-63

*45

4-5

39-15

1202-0

*20

2-5

16-75

219-91

4-5

40-15

1265-0

*22

2-5

18-75

276-46

-48

41-51

1353-0

3-0

18-10

257-30

5-0

43-51

1487-0

* Systt'me International.

Table XXX* — British Standard Castle Nuts. Eeport No. '28 of
THE Engineering Standards Committee.

Diameter

Bolt.

Ins.
(•25)
(•375)
(•5)
(•625)
(•75)
(•875)

Widtli
aeroMH Flatn.

Max.

Mill.

1* (1-125)
1 J (1-25)

H(i-5)

li(1^75)
2

Ins.

•525

•710

-920

1-100

1-300

1-480

1-670

1-860

2-050

2^410

2^760

3^150

Ins.

•520
-705
•915
1-092
1^292
1-472
1-662
1-850
2-040
2-400
2^750
3-140

= es
O 9

X -
C =
t. —

O K

Ins.
•61
•82
1^06
1^27
1-50
1-71
1^93
2-15
2-37
2-78
3-19
3-64

IJD.

Ins.

-31

•47

•63

•78

•94

109

1-25

1-41

1-56

1-88

2-19

2^50

Hcxa-
rtion.

•

s
o

-1

^rtion.

« o

•

"" o

°£

U o

■»*.-<

•"•a

■S-s

O-H

43 ca

»^

•C'O

«.2

0-75 D.

5 >»

Ins.

In.

■19

•12

-45

-03

-063

•28

-19

•64

•05

-094

•38

-25

•85

-06

•125

-47

•31

1^02

-08

•156

•56

-38

1^22

-09

•188

•66

•43

1^400

-11

•219

•75

•50

1-590

•13

•250

•84

-57

1^78

-14

•281

•94

-62

1-97

-16

•313

•75

2-33

-19

•375

1-31

-88

2^68

•22

•438

1-50

1-00

3-07

•25

-500

i«l>-

In.
11
16
22
27
33
38
44
49
55

77
88

APPENDIX

Table XXXI. — British Standard Automobile Threads. Kepokt No. 54

ov thk Enoineebino Standards Committee.

Cross

Full Diameter.

No. of

Threads i>er

inch.

Pitih.

Standard

Depth of

Thread.

Eft'ective
Diameter.

Core
Diameter.

In.

Sectional
Ai-eaat

Bottom of
Thread.

In.

Sq. In.

i (•25)

•0385

•0246

•2254

•2007

•0316

A (-28125)

•0385

•0246

•2566

•2320

•0423

A (*3125)

•0455

•0291

•2834

•2543

•0508

a (375)

•0500

•0320

•3430

•3110

•0760

A (-4376)

•0556

•0356

•4019

•3664

•1054

J (-fi)

•0625

•0400

•4600

•4200

•1385

A (•5fi25)
8 (-625)

•0625

•0400

•5225

•4825

•1828

•0714

•0457

•6793

•6335

•2236

H (-6875)

•0714

•0457

•6418

•5960

•2790

J (-75)

■0833

•0534

•6966

•64H3

•3250

a (-8125)

•0833

•0534

•7591

•7058

•3913

1 (-875)

•01)09

•0582

•8168

•7586

•4520

•« ( 9375)

•0909

•0582

•8793

•8211

•5295

•1000

•0640

•9360

•8719

•5971

'* The Committee reeommen(i that for «;eiienil use this size be dij^pensed with.

Table XX5

CII. BrI'

risH Standard Autoi

lOBILE N

UTS AND

Bolt I

lEADS.

Report No. 54

OF THE

Knoinoeerino Standards Committee.

Diameter
of

Nl'TS AND Boi-is Hkadk.

NUIH.

Bolt Heads.

Width across Fhlts.

Width acroN»
Corners.

IhicknesH.

Thickness.

, Bolt. 1

Max.

Milt.

Approximate
Max.

Max.

Min.

Max.

Mill.

In.

IliB.

Ins.

In.Q.

In.

J (-25)
A (-28125)
A (-3125)

•445

-440

•515

•21

•20

•16

•15

•525

•520

•61

•26

•25

•2:i

•22

•525

•520

-61

•26

•25

-23

•22

i (-375)

•600

•595

•69

•32

•31

•28

•27

A (-*376)

•710

■705

•82

•39

•38

•34

•33

J Q'>)

•S20

•815

•95

•45

•44

•39

•38

A C'^625)
i C^Vio)
H (-6876)

•920

•915

1-06

•51

•50

•45

•44

1010

1-002

117

•57

•56

-50

•49

i (-75)
H (-8125)

1-200

1192

r39

•70

•69

•61

•60

1 i (-875)
*it (-9375)

1-390

1382

101

•82

•M

•72

•71

1-480

1-472

1-71

•89

•88

•78

•77

The Committee recommend that for general use tbiu size be dispensed with.

APPENDIX

Table XXXIII. — British Standard Whitworth Thread. Report
No. 20 OP the Engineering Standards Committee.

Full Dlamet'Or.

»
To

JL
1 a

~1 6

Ins.
(•25)
(•3125)
(•375)
(•4375)
(•5)

(•5625)
(•625)
(•6875)
(•75)
(•8125)
(•875)

IJ (1^125)
IJ (1^25)
H (1-375)
H (1-5)

No. of

Tlireada

per in.

Pitch.

StAndard
Depth of
Thread.

Effective
Diameter.

Core
Diameter.

Ins.

In.

Ins.

•0500

•0320

•2180

•I860

•0556

•0356

•2769

•2414

•0625

•0400

•3350

•2950

•0714

•0457

•3918

•3460

•0833

•0534

•4466

•3933

•0833

•0534

•5091

•4558

•0909

•0582

•5668

•5086

■0909

•0582

•6293

•5711

■1000

•0640

•6860

•6219

■1000

•0640

•7485

•6814

1111

•0711

•8039

•7327

•1250

• •0800

•9200

•8399

1429

•0915

1^0335

•9200

1429

•0915

1^1585

10670

1667

•1067

1^2683

1-1616

1667

•1067

1-3933

1-2866

Area at

Bottom of

Thread.

Sq. Ins.
-0272
•0458
•0683
•0940
•1215
•1632
•2032
•2562
•3038
•3679
•4216
•5540
•6969
•8942
1-0597
1-3001

Table XXXIV. — British Standard Pipe Threads. Report No. 21
OF THE Engineering Standards Committee.

-is

Ins.

2
2i

c ^ .
cd «>3

22 =

In&.

« 7

a V
IX L

-^16

2f
2f
3

Ins.

•383

-518

•656

•825

•902

-041

189

1-309

1-650

1-882

2-116

2-347

2-587

2-960

1
1-

In.
•0230
•0335
•0335
-0455
•0455
•0455
•0455
•0580
•0580
•0580
•0580
•0580
•0058
•0580

a.
B

Ins.
-337
•451
•589
•734
•811
•950
■098
•193
•584
•766
2 000
2^231
2-471
2-844

"55

1
1
I
1

28
19
19
14
14
14
14
11
11
11
11
11
11
11

Nominal length
of Thread.

Ins.

•375

•500

-625

•625

•750

-750

-875

1000

1-000

1-125

1^125

1-250

5 c

Ins.
•75
•75
100
125
1-25
1-50
1-50
1-75
200
200
2-25
2-25
2-50
260

APPENDIX

Table XXXV. — Bbitish Standabd Fine Screw Thbeads. Report
No. 20 OF THE Engineering Standards Committee.

Fiill
IMaiiiet«r.

No. of

ThreadH

])er in.

Pitch.

In.

Standard
Depth of
Thread.

Effective
Diameter.

Core
Diameter.

Area at

Bottom of

Thread.

Ins.

In.

Ins.

Sq. Ins.

1 (-25)

•0400

•0256

•2244

•1988

•0310

(■27)

•0400

•0256

•2444

•2188

•0376

fj (-3126)

•0455

•0291

•2834

•2543

•0508

t (-375)

•0500

•0320

•3430

3110

•0760

iV (-4376)
\ (-5)

•0556

•0356

•4019

-3664

•1054

•0625

•0400

•4600

•4200

•1385

i\ (-5625)

•0625

•0400

•5225

•4825

•1828

1 (-625)

•0714

•0457

•5793

•5335

•2235

H (-6875)

14 .

•0714

•0457

•6418

•5960

•2790

f (-75)

•0833

•0534

•6966

•6433

•3250

if (-8125)

•0833

•0534

•7591

•7058

•3913

h (-876)

•0909

•0582

•8168

•7586

•4520

•1000

•0640

•9360

-8719-

•6971

IJ (1125)

•1111

•0711

10539

•9827

•7585

li (1 25)

•1111

•0711

1-1789

1-1077

•9637

1| (1-375)

•1250

•0800

1-2950

1-2149

1-1593

U (1-5)

•1250

•0800

1-4200

1-3399

1-4100

1| (1-625)

•1250

•0800

1^5450

1-4649

1-6854

If (1-75)

•1429

•1915

16585

1^5670

1-9285

•1429

•1915

1-9085

1-8170

2-5930

2J (2-25)

•1667

•1607

21433

2-0366

3-2576

2J (2-5)

•1667.

•1067

2-3933

2-2866

4-1065

2f (2-75)

•1667

•1067

26433

2-5366

5-0535

•20: :0

•1281

2^8719

2-7439

5-9133

3i (3-25) 5

•2000

•1281

3-1219

2-9939

7^0399

34 (3-5) 4-6

•2222

•1423

3-3577

3-2154

8-1201

3J (3-75)

4-5

•2222

•1423

3 6077

3-4654

9-4319

4-5

•2222

•1423

3^8577

37154

10-8418

•

Useful

Metrical

Equivaleni

rs.

Lbjs. per sq. in. x

0-070308

= kilogs. ]

)ersq. cm.

Tona per aq. in. ><

: 157-49

^^ »t

»»

Kilogs. per sq. ci

n. X 14-2231

2 = lbs. per

' sn{, in.

Kilogs. per sq. m

Btre X 0'20l

) = lbs. per

sq. ft.

Kilogs. per sq. m

m. X 0-635

= tons pe

r sq. in.

1 inch --^ 25-4 mm.

1 mm.

= 003937 ii

1 mile - 1-6093 kiloni

1 kilom.

= 0-62137 n

jile.

1 sq. in. --= 6-4616 sq. ci

1 sq. cm

. =015oeq.

in.

1 cub. in. = 16-387 c.c.

1 c.c.

= 00610 cu

b. in.

1 pint = 0-568 litre.

1 litre

= 1-7598 pi

nts.

lib.

= (

)*4536 kilog.

1 kilog.

= 2-2046 lb

APPENDIX

Table XXXVI. — Logarithms-

• 1-

« 8

•

8 4

•

6 T • 9

0000 1 0048

00£6

0128

0170 1

|0212

02^8

0294

0884

0374

4
4

18 17
6 19 16

26 80 84 38
24 28 82 87

0414

0458

0492

0681

0669

0607

0646

0682

0719

0766

4
4

8 12 16
7 11 16

19
10

28 27 81 85
22 26 80 88

0792

0628

0664

0899

0984

0069

1004

1088

1079

1106

8
8

7 U 14
7 10 14

18
17

21 25 28 32

20 24 27 81

1189

1178

1206

1289

12n

ISOS

1886

1867

1899

1430

7 10 18
7 10 12

16 20 23 26 80
16 19 22 25 29

1461

1492

1528

1668

1684

1614

1644

1678

1708

1782

8
8

6
6

9 12
9 12

16 18 21 24 28
15 17 20 23 S6

1761

1790

1818

1847

1876

1003

1981

1969

1987

2014

3
3

6
6

9 11
8 11

14
14

17 20 23 26
16 10 22 25

2041

2068

2095

2122

2148

2176

2201

2227

2253

2279

8
8

5
6

8 11
8 10

14
18

18
12

16 19 22 24
16 18 21 S3

2804

2880

2856

2880

2406 1 2430

2466

2480

2604

2629

3
2

6
6

8 10
7 10

1618 20 28
15 17 19 2S

25&S
2788

2677

2601

2626

2648

2672

2696

2718

2742

2705

6
6

7 9
7 9

12
11

14 1619 21
14 1618 21

2810

2883

2860
8076

2878

2900

2923

2f»46

2967

2989

2
2

4
4

7 9
6 8

11
11

IS 16 18 20
18 15 17 19

8010

8082

8054

3006

3118

8324
8.V22
8711
3S92

8139

8160

8181

8201

6 8

10 !

10 t
9
9

IS 16 17 19

91
98
98
24

S222
8424
8617
3802

S243
8444
8636
3820

8263
8464
3655

38^8

8284
3483
8C74
3856

3304
3502
8002
3874

3345
3;>4 1
3729
3,X)9

3305
9560
8747
£927

8385
3579
8766
3945

3404
3598
8784
3962

2
2
2
2

4
4
4
4

6 8
6 8
6 7
5 7

12 14 16 18
12 14 15 17
11 13 16 17
11 12 14 16

S979

3997

4014

4031

4048

4065

4232
4:j93
4548
40'jS

4082

4099

4116

4133

6 7

8
8
8

10 12 14 15

26
97
28
29

4150
4314
4472
4624

4166
4830

44S7
4639

4183
4346

4502
4654

4200
48(i2
4518
4669

4216
4378
45M3
46S3

4249
4409
4504
4713

4205
4425
4579
4728

4281
4440
45i)4
4742

42H.S
4450
46(»9
4767

2
2
2

8
8
8
8

6 7
6 6
6 6
4 6

10 11 1315
9 11 IS 14
911 12 14
910 12 13

4771

4786

4800

4814

48:^9

4909
6105
6237
53t6

4843

4983
51 19
5250
5378

4S:7

4997
5132
52oa
5391

4S71

4886

4900

4 6

7 9 10 11 13

81
89
88
84

4914
6051
5186
6815

4928

5065
6198
&8J8

4942
6<i79
5211
6340

4955
bOU2
5224
5353

5011
5145
5276
5403

6024
5159
52h9
5410

603S
5172
5302
5428

3
8
8
8

4 6
4 6
4 5

4 6

7
7
6
6

6
8
6
6

6
6
6
6

6
6
4
4

81011 12
8 9 11 12
8 910 12
8 91011

5441

6458

6465

5478

54iK)

5502

5514

56-27

65S9

5551

4 6

7 9 10 11

87
88

6568
5683
5798
(911

5576
6694
5S09
5922

5587
5705
5821
6033

65J>«»
5717
5832
5944

5«>1 1
572'.»
5843
5955

5023
5740
5855
5960

.'635
6752
5866
5977

1 5647

' 5703

5S77

59S8

W558
5775
5^88
5999

5070
57'<6
6890
6010

2
2
2
2

4 6
8 6
8 5
8 4

7 8 10 11
7 8 910
7 8 9 10
7 8 910

6021

6031

6042

6053

6064

6075

6085

6096

0107

6117

8 4

6 8 910

41
48
43
44

6128
6232
6335
6435

6188
6243

6:U5
6444

6149
6355

6160
62»>a
63r.5
G4o4

6170
(•)2T4
6375
6474

6180
02S4
6385
'^84

0191
GJ94
03*»5
0493

0201
• 304
0405
0503

6212
6314
6415
6513

6222
6325
6425
6522

2
2
2
2

8 4
8 4
8 4
8 4

6 7 8 9
6 7 8 9
6 7 8 9
6 7 8 9

6532

6542

6551

6501

6571

6580

6590

0599

6699

6618

8 4

6 7 8 9

46
47
48
49

6628
6721
6812
690-*

6637
6730
6821
6911

6646
6739
6830
6020

6656
6749
6839
092S

6065
6758
6848
6937

('67.S
0707
6S57
0940

60S4
6770
0m>6
0955

6(J93
6785
(>876
6i»04

6702
6794
6884
6972

0712
6803
6893
6981

2
2
2
2

8 4
8 4
8 4
8 4

6 7 7 8
5 6 7 8
5 6 7 8
5 6 7 8

6990

0998

7007

7016

7024

7033

7042 j 7050

7059

7067

8 8

5 6 7 8

APPENDIX

Table XXXVL — Looabithus — continued

9 |l 9 8 4

6 7 9 9

81
82
83
84

7076
7100
75M8
7884

7084
7108
7251
7838

7098
7177
7259
7840

7101
7185
7267
7848

7110
7193
7375
7356

7118
7303
7284
7804

7120
7310
7293
7873

7136
7218
7800
7880

7143
7336
7303
7388

7153
7235
7810
7896

13 8 8
13 3 8
13 3 8
13 3 8

4
4
4
4

5 7 8
5 6 7 7
5 6 6 7
5 6 6 7

7404

7412

7419

7427

7435

7443

7461

7459

7400

7474

13 3 3

5 5 6 7

87
68

7488
7659
76S4
7700

7490
7500
7042
7710

7497
7574
7049
n28

7505
7582
7657
7781

7513
7580
7064

7520
7597
7073
7746

7528
7004
7079
7753

75S8
7012
7080
7700

7543
7019
7094
7707

7551
7027
7701
n74

13 3 3
13 3 8
113 8
113 8

5 5 6 7
5 6 6 7
4 6 6 7
4 5 7

7788

nso

n96.

7808

7810

7818

7835

7832

7889

7840

112 8

4 5 6 6

88
88
81

7858
7984
7998
8068

7800
7981
8000
8060

7808
7938
8007
8075

7875
7945
8014
8082

7883
7952
8021
8089

7689
7959
8028
8096

7896
7900
8085
8103

7908
7978
8041
8109

7910
7980
8048
8116

7917
7987
8055
8122

113 8

112 8

113 8
113 8

4
8

8
8

4 5 6
4 5 0.
4 5 5
4 5 5

8120

8186

8143

8149

8215
8280
8844
8407

8156

8163

8109

8176

8183

8180

113 8

4 5 5

67
68

8195
8201
8886
8888

8202
8207
8881
8895

8200
8274
8888

8401

8223
8287
8351
8414

8328
8298
8357
8420

8285
8299
8303
8420

8241
8800

8870
8433

8248
8813
8876
8489

8254
8819
8388
8445

113 8
113 8
113 8
113 2

8
3
8

3
3
8

8
8

3
3

3
3
8
8

3
2
2
2

2
2
2
2

2
2

4 5 5
4 5 5
4 4 5
4 4 5 6

8461

8457

8408

8470

8483

8488

8491

8500

8508

113 2

4 4 6

71
78
78
71

8618
8678
8088

8003

8510
8570
8089
8008

8585
8585
8845
8704

8531
8591
8051
8710

8537
8597
8057
8710

8548

8003
8003
8722

8549
8009
8069
8727

8555
8015
8075
8733

8501
8621
8681
8739

8507
8027
8680
8745

112 2
112 2

112 3

113 2

4 4 5 5
4 4 5 5
4 4 5 5
4 4 5 5

8761

8766

8788

8708

8n4

8779

8785

8791

8797

8803

118 8

3 4 5 5

78
77
78

8i08
8806
8921
8976

8814
8871
8927
8983

8820
8870
8932
8987

8825
8882
8988
8998

8881
8887
8943
8998

8887
8808
8940
9004

8842
8899
8954
9009

8848
8904
8960
9015

8R54
8910
8905
9030

8859
8915
8971
9025

113 3
113 3
113 3
118 2

8 4 5 5
8 4 4 6
3 4 4 5
3 4 4 5

0081

9036

9043

9047

9058

9003

9009

9074

9079

113 2

3 4 4 5

81
88
88
81

9086
9188
9191
0848

9000
0148
9196
9348

9096
9140
9301
9258

9101
9154
0200
9258

9106
9159
9212
9208

9113
0105
9217
9209

9117
9170
9222
0274

9123
9175
9237
9279

9128
9180
9232
9284

9133
9l8:i
923S
9289

112 3

112 2

113 2
113 3

3 4 4 5
8 4 4 5
3 4 4 5
8 4 4 5

0804

0200

9804

0309

9316

9320

0325

9330

9385

0340

112 2

3 4 4 5

87
88

0846
9895
0445
9494

0350
9400
9450
9499

9356
9405
9455
9504

9300
9410
9400
9509

9305
9415
9405
9513

9370
9420
9409
9518

9375
9425
9474
9523

9380
9430
9479
9583

9385
9485
9484
9533

9390
9440
9489
9538

112 2
112
112
112

3 4 4 5
3 3 4 4
3 3 4 4
3 3 4 4

0643

9547

9553

9557

9502

9500

0571

9570

95S1

9580

112

3 3 4 4

01
93
93
9f

9590
96S8
9085
9731

9595
9643
9089
9736

9000
0047
9094
9741

9805
9652
9699
9745

9009
9057
9703
97i>0

9014
9061
9708
9754

9019
90J0
9713
9759

9024
9071
9717
9703

9028
9675
9722
9768

9633
96S0
9727
9773

112
112
112
112

3 3 4 4
3 3 4 4
3 3 4 4
3 3 4 4

9777

9782

9786

9791

9796

9S00

9805

9809

9814

9818

112

3 3 4 4

07
08
00

9828
»b68
9918
9956

9827
9872
9917
9901

9832
9877
9^21
9965

9S30
9881
9920
9909

9841
9SS0
9930
9974

9845
9890
9934
9978

9850

9894

9939

.9988

9S54
9S99
9943
9987

9859
9903
9948
9991

9863
9903
9952
9990

112
112
112
113

3 3 4 4
3 3 4 4
3 3 4 4
3 3 3 4

M.C.E.

C C

APPENDIX

Tablb XXXVIL — Tbioomohbtrical Ratios.

Angla.

Cliord.

Sine.

Ikngent.

Ck>-taiigent

OoRioe.

De-

grcM.

Bftdiana.

0»

«o

1*414

1-5708

OOP

1
S
8

•0175
•0349
•0524
•0098

•017
•035
•058
•070

•0175
•0349
•0528
•0698

•0175
•0349
•0524
•0699

67^2900
28*6368
19 0811
148007

-9998
•9904

•9986
•9976

1^402
1^889
1^377
1-864

1-5588
1-5S59
1-5184
1-5010

89
8S

87
8d

•0878

•087

•0872

•0875

11-4301

•9962

1^85l

1-4885

6
7
8

•1047
•1222
•1890
•1571

•105
•122
•140
•157

•1045
•1219
•1892
•1564

•1051
•12-28
•1405
•1584

0^5144
8^1443
7^1154
6^3138

•9945
•9<.>25
•9908
•9877

183S
1-8-25
1-312
1-299

1-4661
1^44S6
1*4812
14137

84
88
82

•1745

•174

•1786

•1768

6-6718

6-1446
4^7046
4*8815
4^0108

•9848

1-286

1-8963 80

11
18
18

•1920
•2094
•2209
•8448

•192
■209
•226
•244

•1908
•2079
•2250
•2419

•1944
•2126
•8309
•2498

•9310
•9781
•9744
•9708

1-272
1-259
1-245
1-231

1*3788
1^3614
1*8439
1 •3*265

79
78
77
76

•2618

•261

•2588

•2679

8-7821

•0659

1-218

1-3090 1

16
17
18
19

•2793
•2967
•8142
•8816

•278
•296
•818
•830

•2756
•2924
•8090
-8256

•2867
•8057
•8249
•8448

8*4874
82709
8-0777
2-9042

•9618
•9563
•9511
•0455

1-204
1-190
1176
1-161

1-2916
1*2741
1-2566
1-2392

74
78
78
71

•8491

•847

•8420

•8640

87476

•9397

1*147

1-2217

81
28
28
24

•8665
•8840
•4014
•4189

•864
•382
•399
•416

•8584
•8746
•8907
•4067

•8839
•4040
•4245
•4453

2*6051
2^4751
2*3659
2*2400

•9336
•9272
•9205
•9185

1-138
1-118
1*104
1-089

1-2048
1-1808
1^1694
11519

60
68
67
66

•4368

'438

•4226

•4668

2-1445

■9068

1075

1^1845

8ft
27
28
29

•4538
•4712
•4887
•6061

•460
•467
•484
•601

•4884
•4540
•4G95
•4848

•4877
•5095
•6317
•5548

2-0508
1-9626
1-8807
1-8040

•8988
•8910
•8829
•8746

1-060
1-045
1*080
1-015

1^1 170
1*0996
1-0821
1-0647

04
63
08

•5236

•518

•5000

•5774

1-7821

•8660

1-000

1^0172

81
82
88
84

•6411
•6585
•6760
•6984

•534
•551
•568
•585

•5160
•6299
•5446
•5592

•6009
•6-249
•6494
•6745

1^0643
1^6003
1*5399
1-4826

•8572
•8480
•8387
•8290

•0S5
•970
•954
•939

1-0297

1-0123

-9948

•9774

69
58

•6109

•601

•5786

•7002

1*4281

•8192

•923

-0599

80
87
88
89

•6283
•0468
•6632
•6b07

•618
•635
•651
•063

•5878
•6018
•6157
•6298

•7265
•7536
•7818
•8098

1*3764
1-3270
1-2799
1-2349

•8090
•79S6
•7880
•7771

•908
-892
•877
•861

-9425
•9250
-9076
•8901

54
53
58
51

•6931

•0S4

•6428

•8391

1*1918

•7660

•845

•8727

41
48
48
44

•7156
•7330
•7505
•7679

•700
•717
•733
•749

•6661
•6091
•6820
•6947

•8693
•9004
•9325
•0637

1-1504
1-1106
1-07-24
1*0355

•7547
•74ai
•7814

•7193

•829
•SI 3
-797
•781

•8552
•8378
•8203
•8029

40
48
47
46

45«

•7854

•765

•7071

1-0000

10000

•7071

•765

•7854

45»

Cosine.

Co-Unsent.

Tangent.

Sine.

Chord.

Uodlans.

I>e-
greee.

Angle.

INDEX

Acceleration diagrams, 155

„ uniform, 142

Accelerometers, 79
Air cooling, 238

„ resistance, 84
AUoy, steel, 45.
Alternating stresses, 25
Aluminium, 52
Angles of cone clutches, 249
Annealing, 49

Arrangement of gearbox, 304
Attachment of gudgeon pin, 165
Axles, casing of, 344

fixed, 351

live, 323

loads on, 326

swivel, 362

>»

»»

t»

>»

Babbitt metal, 51
Balancing of engines, 199

of single rotating mass,

200
of two rotating masses,

201
reciprocating parts, 210
reference planes, 202
secondary, 214
six -cylinder engine, 217
Bearings, load carried by, 318

„ metals, 52
Bending moments, 16
Bessemer process, 42
Bevel wheels, 282

drives, 316
efficiency, 92
Brakes, 259

cams for, 266
design of, 262
for road wheels, 260
operating gear, 261
springs for, 267

Cams, 139

„ design of, 141

»»

>»

»»

♦ »

Cams for brakes, 259
Camshafts, 152

„ chain drive for, 149
Cast iron, 34

„ „ malleable, 37
Chain drives, 293

„ „ design of, 294

Clutches, design of, 248

cone, 249
disc, 251
plate, 253
springs for,
256

Columns, strength of, 15
Cones on shafts, 326
Connecting rods, 163

Gordon's formu*

I», 169
inertia of, 167
load on, 167
Consideration in design, 7
Cooling, 55

„ air, 238
„ water, 239
Crankcases, construction of, 222
material for, 221
suspension of, 228
Crankshafts, couplings for, 191
design of, 178
material of, 186
tortional rigidity, 1 92
webs, 172
Cycloidal cutters, 274

»»

»>

»»

»>

»»

»>

Design of axles, 323—352

„ casings, 344
bevel wheels, 316
brakes 262

„ cams, 266
„ sprinffs, 267
cams, for valves, 141
camshafts, 152
chain drives, 294
clutches, 248

cone, 249

»»

>»

f f

»'

>•

»»

INDEX

>»
>>
f»
>»
>>
»»
»i
»f
>»
>»

»>
>»
»»
>>
f»
»»
»>
»»

Design of clutches disc, 251

„ plate, 263
,, springs for, 255
columns, 15
connecting rods, 163
couplings, 326
crankshafts, 178
frames, 337
flywheels, 197
valves, 126

„ springs, 145
worm drives, 316
Determination of engine dimen-
sions, 100
Diagrams of acceleration, 155
Duralumin, 53

Efficiency of bevel wheels, 92
„ „ transmission, 91

„ „ worm gearing, 93

Elasticity, modulus of, 12
Empirical formulsB, 9
Engine an*angements, 75

„ cooling, 238

„ dimensions, 100
Estimation of power required, 96
Exhaust ports, 126

Factor of safety, 22
Flywheels, 196

energy stored, 197
size of, 197
stress in, 196
Frames, construction of, 328
design of, 337
factor of safety, 337
loads on, 329
Fuel systems, 247

»>

»»

>»

»>

Gearboxes, 221

material, 221
shafts, 312
suspension, 228

Gearing, 270

change speed, 302
cycloidal teeth, 273
helical, 284
involute teeth, 275
ratios, 309
„ worm, 285
Geometrical properties of steering
gears, 357

>»

99
99

»»

»>

Gordon's form ulsB, 15
Gudgeon pins, 162

Hardness tests, 28
Harmonic motion, 144
Helical gearing, 284
Hook's law, 12

Horse-power form ulse, I. A.E. Com-
mittee, 66
B.H.P.,101
cylinder^
dimensions for, 107

>»

»»

Ignition, type for, 72

Impact tests, 28

Importance of good valve gear, 135

Inertia of connecting rods, 167

Inlet and exhaust piping, 245

„ valves and ports, 126
Involute teeth, 275

„ cutters, 276
Iron ores, 32

„ cast, 34

„ malleable C.I., 37

„ wrought, 41

Jackets, 126

Keys, 326

Live axles, 323

Loads, classification, 335

diagram for valve gear, 155

fluctuating, 25

on transmission gear, 297
Lubrication, 56

>»

»>

Manganese bronze, 52
Measuring pitch, 277
Metric units, 9
Moments, bending, 16

Nickel steel, 47
Oil pumps, 235

Pedals for brakes and clutches^
258

INDEX

»t

Piping, inlet and exhaust, 245
Piston coDBtruction, 159

number of rings, 160

material, 159

speeds, 106

thickness, 161
Poi8son*8 ratio, 13
Power, estimation of, 96
Pressure, mean effective, 104

„ of compression, 71
Profile of carriages, 87
Propeller shafts, 315

„ „ brakes, 264

Pumps, oil, 235
„ water, 240

Radiators, 243

„ size of, 244

Radius rods, 355

Resilience of materials, 14

Resistance, 77

air, 84
gradient, 83
road, 81

»»

>»

»»

Sajstt, factor of, 22
Springs, clutch, 257

design of, 348
helical, 344
periodicity of, 350
resilience of, 350
Standardisation, 8
Steel, 40

Steering gear, columns, 366

errors, 361
geometry of, 357
levers, 362
Strength, compression, 14

»»

»>

>»

Strength, shear, 15

„ ultimate, 13
Stress and strain, 11
Studs and bolts for cylinders, 132

Tappets, 138

Teeth of wheels, cycloidal, 273

involute, 275
proportions, 279
shape of, 271

Timing of valves, 135

Torq^ue rods, 355

Torsion, 21

Torsional rigidity, 192

Transmission efnciency, 91
„ gearing, 297

Twistinff moments, 22

Types of gear, 271

»»

9»

»»

Uniform acceleration, 142
Universal joints, 298

Valves, arranffement of, 148
size of, 126
sea tings for, 131
sprinffs for, 145
steel for, 130

Volume of gear pump, 236

»>

»»

Water cooling, 239

„ jackets, 126

„ pumps, 240
Webs of crankshaft, 186
\Mieel base, 332
Worm gearing, 285

design of, 289

THB WBITEPRIAR.S PRBS8, LTD., LONDOif AND TUNBBIDGI.

dIaOaB*

D D

8 5 3 1 ,s

14 DAY USE

RETURN TO DESK FROM WHICH BORROWED

LOAN DEPT.

This book is due on the last date stamped below, or

on the date to which renewed.

Renewed books are subject to immediate recalL

•^f%

'V.

1 1

HU est Jill. 81987

^r^A

^0^

^^P^

AUG 06 1987

^nmM^

Am " t ^^ ^ ^

NQV1 1

AUTO DISC

ves?

JJI UTO . DISC APR 1 A '87

AUG 06 1987

LD 21A-45m-9,'()7
(115067810)4763

General Library

Univenity of California

Berkeley

YC 19386

U C. BERttlEY UBRMIIB

■iiiiiinin

;>■'.

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